I would contact the DNR like other have mentioned. No need to shoot them since they can be live trapped and relocated. River otters were extinct in Indiana and the DNR has been working to re-populate them. It has gotten to the point in some areas there is a limited trapping season like Cevans mentioned.

If you have the problem with muskrats, Google a local fur buyer near you and get the name of a trapper. He would gladly take them off your hands. He makes a few dollars and you get your levy saved.