Crayfish do not have a specific possession limit, however you can only have up to 5 traps at one time without obtaining a commercial fishing license and trap tags.
This is from the 2012 fishing regulations:
Trapping or Seining Minnows and Crayfish:
Nongame fish (minnows), yellow perch, and crayfish may be taken only
in waters open to fishing; provided the seine or net does not
exceed ten (10) feet in length or width, and nets and seines
must have three-eighths (3/8) inch square or smaller mesh;
and the minnow or crayfish trap does not exceed two (2) feet
in length, width or height. If the trap is of irregular dimension,
but its volume does not exceed the volume of an eight (8) cubic
foot trap, it is also legal to use. Nets and seines may not be
left unattended. Traps must be checked at least every forty eight
(48) hours. All traps must have a tag attached bearing the
owner’s name and address.
All game fish (except yellow perch) and protected nongame
fish incidentally taken while trapping or seining must be
immediately released alive. All fish so taken must immediately
be killed except where stated otherwise. Crayfish may be kept
alive to be used as bait only on the water where captured.
Nongame fish and crayfish may only be taken during the season
set for the taking of game fish in those waters.
Only five (5) crayfish traps can be fished with a valid fishing
license. If more than five traps are used at one time, you must
obtain a Commercial Fishing License and trap tags.
It is illegal to destroy, disturb, or remove any traps belonging to