My t would rarely bring it up in session, but I still did freely. There was never a spoken rule about reporting self-harm, but as a client I get freedom in what is said and not said in a session, so thus I bring up self-harm with out being prompted.
If I cut myself normally I would go right into session and say it off the bat. I figured in going so my t and I could work out the details and talk about it when there was enough time. Without being asked I would tell her what lead to it and if I tried to prevent. She would ask where, with what and if I was really meaning to kill myself at the time.
At the end of a session, every session without a fail, she would say, "Please take care of yourself and call me if you need me." The self-harm concerned her and she once or twice told me that she was concerned that I would cut too deeply and need stitches or die. She took the self-harm and its triggers very seriously.
Sorry this was so long.