This response is given for informational purposes only.
The first thing I would suggest is to consult the person's sentence, if the person is still under sentence, to see if there are any specific provisions in his sentence that prevent him from owning a bow and arrow.
That said, there is no statute that comes to mind that would stand in the way of owning a bow and arrow, even by a convicted felon.
Still, it would never be a bad idea to consult an attorney with the specific facts surrounding this situation to be sure.
As a general rule, probation orders only prohibit the probationer from having a firearm, but the safer bet is to review the sentence or better yet, check with the probation officer to be sure. If the person thinks the prohibition is in error, a motion to modify the sentence can be filed with the judge although those motions don't have a high success rate.