My friend at work was accused of sexual harassment. Does he have to sign the form that HR gave him?

Does he have to sign the form that HR gave him to acknowledge he was spoken to? The form does not have any details of what actually happened. That is why he does not want to sign the form. What will happen if he doesn't sign it?

I would sign it but add a note that signing in NO WAY indicates an acceptance of the scenario or any guilt on his part. I would also make sure that he is given copies of ALL paperwork pertaining to the issue.

He could always sign it, but add in a note that his signature does NOT acknowledge or admit guilt but only that he was spoken to regarding the situation.
And ask for a copy as soon as he signs it so they cannot 'add' anything to it.

No, but the form really doesn't say he agrees with anything, just that he was informed.

He can even write something on the form to that effect and then initial it.

All he is signing is that the HR people did their job and notified him of what happened, he is not signing a confession.

I don't see any problem in signing it. I would write on it that signing it is not an admission of guilt and insist on getting a copy.

"Your friend" should sign it.

Assuming he does not have an employment contract, they can fire him right now if they want. If he doesn't sign it, he will be fired. Even if he does sign it, he could be fired. They absolutely can make him sign it and they can fire him. He's basically screwed.

It depends what is says. If the information is wrong, don't sign. If it's simply a notice from the company stating their policy, sign it - it's a reasonable request and you can be fired for cause if you refuse.

However, sexual harrassment law can get complicated and unpleasant very quickly. He might find the best thing to do is contact a lawyer with experience in this field, and ask the lawyer to request a meeting between HR and all interested parties. That's usually enough to make HR back off unless there is a strong case against your friend.