@weeveeship if you called the cops then they might want you to sign a complaint, but there are no compulsions to do that. Even if you do sign a complaint (this is all very preliminary; there may not even have been an arrest yet), you are not obligated to be a prosecution witness. (However, if you are a “material witness”, then I think that you can be compelled to testify at a subsequent trial, if one is held. I’m not certain of the legal definition of “material witness”, so that might be worth looking up.)
For most misdemeanor offenses such as “fighting in public” (assuming no one is killed or gravely injured, and no one other than the police presses charges), there may not be a trial, as @heresjohnny suggests. The thing would be plea-bargained down to some type of “nuisance” charge and the sentence (at least for a first-time offender) would likely be “time served” (waiting in the lockup for arraignment, for example). For a non-first timer, there may be charges brought, but the cost of a trial would still compel the District Attorney to bargain for some kind of agreement with the offender, with a resulting lighter sentence that a judge would sign off on.
If the offense happens in a “three-strikes” state, and this is a repeat offender (if one of the combatants is identified as an instigator or even a target of a prosecutor’s wish to “clear the streets”), then there may be a formal trial with “full measure of the law” brought, in order to put the guy away for life. (The vagaries of our system, sometimes.)
Calls can still be made anonymously from public phones, and you could always say that your phone was not in your possession when a call was placed. Even calls from one’s home phone can be explained as “not by me”, if the potential for multiple callers exists, such as at a party, for example.