My rule of thumb... a psychopath wouldn't care enough about being one to really even ask the question. It's just how they are. The lack of conscience makes the lying a whatever thing to them. They don't care enough about the feelings of other people to worry about how their own behavior is affecting anyone.

I've also read, like the other comment, that people with antisocial personality disorder (what psychopaths technically are diagnosed with) don't have things like depression or suicidal tendencies.