Are there any rules governing relics?

You may keep the relics for veneration or give them away. You may not sell them: "It is absolutely forbidden to sell sacred relics" (canon 1190 §1). This applies to all authentic relics of saints.

The New Commentary on the Code of Canon Law notes that the code expresses this prohibition in its strongest language, nefas est, "it is absolutely forbidden." Owners may give relics away, except for a second category that needs the Apostolic See's permission.

That category covers very significant or highly honored relics. Canon 1190 §2 says relics of great significance, and others greatly venerated by the people, cannot be validly alienated in any way or permanently transferred without the Apostolic See's permission. The commentary explains that the previous code defined a significant relic as a part of a saint's body, such as an arm, forearm, heart, tongue or leg, or the part of a martyr's body that bore the fatal wound, provided it was entire and not too small.