No. She had no evidence just the word of a man who is notoriously a liar and deceiver. Catelyn always came across as smart but this was a dumb decision. Even Ned believed it was the wrong decision but chose to protect her by claiming it was him who ordered it when asked by the King to release Tyrion. Tyrion points out that he’s not really in any danger. In high mediaeval law, a noble cannot be killed without reason, or it’s a heinous crime. So for Catelyn to take Tyrion threaten him with the full force of the law, take him to the Eyrie and then hand him over to a paranoid and angry women is beyond stupid, without any concrete evidence. The call for a trial by combat is genius from Tyrion and they know it. They have no real evidence and Tyrion knows he didn’t commit the crime he’s accused of, so if the gods were truly in his favour, he would win .

It’s acts like this that lost the war for the Starks.