Can people use their influence to find the identities of Twitter users?

[Jessica]

I was having a discussion on Twitter with a person I have never met (about movies). When I ignored this person's advances and focused on the discussion, they quickly became rude and insulting. Before I blocked this person they said they would use their connections in law enforcement to get me in trouble.

I doubt he can do that. Freedom of speech and all that; plus, people make crazy claims on Twitter all of the time.

But it made me wonder: can people with connections or with celebrity influence track their Twitter users if those users tick them off? I'm talking about cases where Twitter users say nasty but non violent or threatening things to celebrities or wealthy influential people.

I know the likelihood of someone tracking down a Twitter user through official means are slim - maybe I'm wrong? - but what about using connections, like police officers who owe you a favor or people at an ISP who might be starstruck by you?

Could a celebrity track down their harasser?