I can't find where it is listed as a game fish or not in the regulations.
Catfish are game fish so you can not use a bow to harvest them.
IDAPA 13.01.11.004. Gamefish: Brook, brown, bull, cutthroat, golden, lake, rainbow (including steelhead), splake and Sunapee trout; trout hybrids; Chinook, coho, Atlantic, and kokanee (blueback) salmon; grayling; whitefish; cisco; crappie; perch; bass; catfish; bullhead; sunfish; sturgeon; northern pike; tiger muskie; walleye and sauger; and burbot (ling). Bullfrogs and crayfish are also defined as game fish.
IDAPA 13.01.11.201.01 says: Archery and spear fishing: Fishing with a bow and arrow, crossbow, spear or mechanical device, excluding firearms. This type of fishing is permitted only in the taking of bullfrogs and unprotected nongame fish and only in those waters during the season set for the taking of game fish.