Definitely get proof from their doctor about their medical condition
USCF How to handle a disruptive player as a TD

I would request proof. If you haven't yet, I would suggest reading through this: https://new.uschess.org/sites/default/files/wp-thumbnails/2020/04/Accessibility-Guidelines-April-2020.pdf

Depending on the nature of the disruptiveness, you could ask the player to leave for the remainder of the event, but tell him he's welcomed to return to play in a future event when he think he's better able to control his actions. Or if he isn't disruptive while observing, you could tell me he's welcome to remain as an observer, but can't play the rest of the event. Or if he's likely to regain his composure, you could forfeit him only for that round and allow him to play in a subsequent round after he's regained his composure.
No matter which route you take, it's better to do it privately and without causing undue embarrassment for the player.

Page 10 of the Accessibility Guidelines clearly states what to do with a disruptive player who claims their behavior is due to a medical condition. See the section "7. Players Displaying Disruptive Behavior."
1. Muttering loudly or repeatedly slamming the pieces is NEVER appropriate behavior at chess tournament, with or without a disability. Warning and eventual forfeiture are possible.
2. It is the player's responsibility to discuss any accomodations prior to the tournament or at least before the first round. Lacking such a discussion, the TD has no choice during a game but to apply standard tournament practice. The opponent has the equal right to proper playing conditions. A discussion about accomodations could be held after the game, depending on the TD's other duties.
3. The player is under no obligation to share proof of their medical condition. However, the TD should ask what behavior plan they have from a healthcare professional. In short, this plan should detail methods that the player calms down and ceases to disrupt others.
Good luck!
Michael Aigner, member of the committee that wrote the above mentioned guidelines

Thank you all for the Accessibility Guidelines, those look like they will definitely be a good resource.

@fpawn is there a more recent version than what I posted? I am not seeing where a player for a documented medical condition is not required to provide proof to receive accommodations. This is from page 11 (of the version I posted above):
This is what I see for section 7:

That's a tough one.
2. It is the player's responsibility to discuss any accomodations prior to the tournament or at least before the first round. Lacking such a discussion, the TD has no choice during a game but to apply standard tournament practice. The opponent has the equal right to proper playing conditions. A discussion about accomodations could be held after the game, depending on the TD's other duties.
I was cursed at by my opponent in front of the tournament director and at least 6 players last month at a tournament. My tournament director kept characterizing what was going on as an argument when one of my opoenent's complaints was that I went directly to the tournament director?! I'd asked him to comply with the rules, then one of the tournament directors asked, and only after he was still not complying did I go to the Chief Director. When he dropped an f bomb to me while the tournament director was telling him to comply, I refused to resume the game and left the board, the director wasn't able to get the player away from the board and the situation was finally resolved by my opponent withdrawing from the tournament. They, my opponent and the tournament, ruined the entire event for me. I was just too upset to concentrate!
I saw the reference to parents and coaches. Too often I see tournament directors being soft on infractions even at money tournaments. They want to do everything to keep the game going even when it's obviously not fair to the poorly behaved player's opponent. Crocodile tears and insincere apologies are typically followed by other less conspicuous forms of unsportsmanlike conduct ie giving the opponent the brow finger, soundlessly mouthing obsenities or insults, even false accusations. If it is not brought to the tournament directors attention before the 1st round, enforce the rules!
Moving that board to a less intrusive location and an empathetic 3 and done warning agreement with the potentially disruptive player seem to be about the best a tournament director could do. After the 2nd warning, I think it's only fair to ask their opponents indulgence but if the 3rd infraction occurs, there doesn't seem to have been any more that could be done.
I'm a local director.

@fpawn is there a more recent version than what I posted? I am not seeing where a player for a documented medical condition is not required to provide proof to receive accommodations. This is from page 11 (of the version I posted above):
This is the version that I see too. Where does it say that a player must submit evidence of a medical condition? I don't believe the document states this either. I understand some tournaments do require proof from all participants as part of registration, e.g. the US Blind.
Ultimately, the tournament director can ask and the player can respond as he pleases. Most people will try to cooperate. However, nobody should be forced to submit proof of a medical condition, unless it is stated in the publicity and applies to everyone. Of course, the director can take the lack of documentation into account when determining a reasonable accomodation. This is where the behavior plan becomes more relevant (referring back to the original post). I should add that there is a huge difference between a visually impaired player who asks to use a standard peg board and someone who repeatedly disturbs their opponent and other players.
All of the discussion about reasonable accomodations should take place privately before the tournament day and most definitely not during a round.
Michael Aigner

I was cursed at by my opponent in front of the tournament director and at least 6 players last month at a tournament.
In more than 30 years, I have never seen a player forfeited because of one verbal outburst. The rule book gives the director wide discretion, but also recommends an escalating penalty system: warning, time deduction, forfeit. You are right that most directors use forfeit as a last resort and tend to err on the side of giving more warnings and time penalties. Indeed, many chess players do get heated and emotional. Geez, I recall watching a player throw a piece at his opponent (after being checkmated) and still continue the tournament.

I've only seen a couple forfeits for conduct and they all happened away from the board. Here's a blast from the past.
. . .
World Open organizer Bill Goichberg expelled Akeem from the tournament when he was accused of striking 14-year old phenom IM Hikaru Nakamura (2511) in an altercation. Goichberg ruled against Akeem (1729) when he discounted witnesses supporting the contention that Hikaru initiated the incident.
. . .

I'm leaning toward a slight separation but not so far that the opponent might be suffering in isolation with the offender. We are a small club and generally the few TDs are also players.
Beyond that I'm probably going to follow general recommendation of warning, and time penalties. Hope this can encourage the player to compose themselves as they generally take chess very seriously.
As a USCF club TD, I have a player who can cause disruptions both verbally by muttering to themselves in a fashion that can be heard by all the player in the small hall. Or by slaming the pieces and/or clock on occasion?
I am aware of the various rules around disruptions including 20N1, however after having spoken to this player about the behavior, they have claimed that it is due in part to a medical condition. We want to be careful to not discriminate against this player, and have considered moving them to a different playing area, but we are concerned about it still affecting their opponent.
Does anyone have any advice, or is there a more appropriate forum to discuss this type of issue.