in most workplaces, employers must typically follow "progressive discipline", where they must keep a paper trail of them warning you about unacceptable behavior and the consequences if you continue. it varies from state to state, and there are usually recognized exceptions (eg committing a crime, gross negligence, etc). this protects them from frivolous claims of ignorance of a situation by the employee, and gives the employee leeway in the event of ambiguity or misunderstanding.

for something like this where a co-worker supposedly felt "uncomfortable", employers would almost always start by moving desks or work areas apart, advising each person to avoid contact with the other, etc. this is often difficult in small teams or small workplace offices, but it is the gesture that is important. i'm not a lawyer (and this is more HR policy than law anyways), and it does vary from region to region, but that's my HR experience in a nutshell.