As we saw in Double Exposure when Roger White tried to blackmail Dr. Kepple, Kepple told him he would have to sign a document detailing their agreement since he is now an accessory after the fact, so I think Karen Fielding became one as well. Whether or not Columbo would have also pursued her is open to debate, but I think she would have gone down if she maintained her story if called as a witness at the trial, if there were one.
I don't think there would be a trial because at the end, Columbo asked Adrian would sign a confession and he said yes. So it seems to me that Adrian was happy when he was finally caught. It meant that he would be away from Karen and his guilt would be relieved. I didn't like when Columbo "flirted" with Karen when he first went to meet Adrian. That wasn't nice.