Aleesha,
Re your message below:
Hi! I'm new here, first post and all.
I have a character that has been on the run for a murder wrap for two years. Would they have had a trial for him? How would that go? Would they use a public defender? 
Welcome to MWF. I think it's a great group. I hope you'll like it.
Regarding your question, in general, trials
in absentia are not allowed in the United States or any other country whose law is based on British Common Law, since it is a violation of the common law principkle of
audi alteram partem or "hear the other side."
There is an exception. If a trial, at which the defendant is present, has started, and the defendant books while the trial is in progress, than the trial can proceed to its conclusion without the defendant being present. In such a case, the defendant would, I suppose, be represented by private counsel if he'd retained private counsel, or by a public defender if he couldn't afford to hire his own lawyer.
Of course, you could always make it that your character escaped from custody
after his or her trial (think the TV series or movie
The Fugitive), in which case the whole question of a trial
in absentia wouldn't even be an issue.