Okay, this is me going from memory:
Pre-Crisis: I think she was arrested in maybe her 3rd appearance as Catwoman. I know there was one where memorably Batman is like lecturing her and she's like "Oh just shut up and take me to jail already"
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Post-Crisis: She got pinched as a street thief and sent to a reform school for young girls that she eventually broke out of. She had a record during her dominatrix Frank Miller days but she had it erased when she reinvented herself as a high society girl. Eventually post-NML Gordon put out a manhunt to finally catch her and she was unmasked but this was coming after Selina Kyle had publicly "died" so no one knew it was her, she was just labeled as a "Jane Doe" and sent to a mental institution.
New 52: She was arrested in the first arc of her New 52 run but her prints came back with nothing, so presumably she'd had her records wiped again. She was also arrested in the Frank Tieri run in the last few issues of her New 52 run when she went to Bruce for help but Bruce, having been made amnesiac by Endgame, turned her in to the police.