No. Parliament is free to choose what it wants to do.
If you find a breach of privilege, I believe that the House can refer the matter to the civil authorities and that they can pursue it from then on. A court looking at it could take note of the proceedings of Parliament, and in that sense the record of this committee would be before the courts. The records of this committee would certainly be available for any police investigation.
I'm not sure that answers your question, but I think the role of this House in the matter ends with a report from this committee and what the House does with it. If the House felt that it was a criminal act that should be dealt with as a criminal act, it could be simply be, as I say, referred to the civil authorities.