whatever state you are in you should first check with your local
Conservation officer or game warden. Muskrats as stated on an earlier
post are furbearers who can usually only be taken by licensed trappers
during open trapping season. However, local CO's may often give
exceptions to animals causing damage to property. If you don't know
how to get ahold of a Conservation officer, call your local police or
sherrif's dept.
Better to be safe than get a ticket for taking an animal out of season
or without a license.

Any wildlife that is wreaking havoc, or can damage (or is causing
damage to) property can be taken out of season with no license needed.

The CO, or DNR, person will tell you this. You do need to contact them
though before doing this.

We are going through this right now with muskrats that moved into our
livestock pond last fall. 1 has been caught so far.