united-states
If this is a private library, yes
A private organisation can ban anyone from their premises providing that the reason is not or is not a proxy for a protected characteristic.
Engaging in a "verbal altercation" is not a protected characteristic so, absent other information, this would be fine.
If this is a public library, yes but ...
Specifically, a public library (or another public facility) could ban a disruptive individual and they would not need to involve law enforcement.
However, for such a ban to be effective and enforcable:
- the ban must be for a good reason. "Verbal altercation" if it rises to the level of abuse of staff members is probably a good reason.
- reasons for banning should be applied universally. It's not permissible to ban one person for the same behaviour that is tolerated from another. Of course, "verbal altercation" covers a wide range of behaviours from testy petulance to assault.
- the person banned must have a chance for their side of the story to be heard and considered. This would include whether a ban based on "hearsay" is appropriate - that is, behaviour reported to the banner by third parties rather than being directly witnessed. The process is unlikely to be as formal as a court so strict rules of evidence like the hearsay rule are unlikely to be required.
- the ban cannot be in response to the exercise of a First Amendment right. The First Amendment protects the content of speech but can be restricted in time, place and means of expression: for example, this is a library, a person who yells or shouts in a library is not protected by the first amendment.
- the public facility must provide a means of conducting essential business. Some functions of a library might be considered essential, others not. For those that are, the library must make appropriate accommodations - like allowing you to access those if you wear a mask.
