I think it was good that this female officer was able to trail the perp and eventually get him put away where he belongs.
The problem I see is if she was knocking on doors and screaming she was a officer who's gun was stolen, how would the average citizen take that? She could be considered lunatic perhaps, doors wouldn't be opened, in general she may be ignored (or he if it was an off duty male officer who had his wallet stolen). Calls could be put in to the police dispatch about a crazy or deranged woman parading as an officer. I just see too many problems here.
I feel she should have done as she did by trailing him to where he was & calling it in to dispatch. Even that act, without a weapon, was dangerous. Anyone else see problems here? How should this have properly been handled?