Occasionally I receive calls from people wanting to store their pets.  As a general rule, most storage facilities will not allow you to store any organic material, live or dead.  Why would someone want to store a pet in a storing rental unit?  I could not tell you why.  I can tell you that it is neither allowable or ethical.  If you need a place to store your pet, you should take a look at using a pet boarding company.  Your pet will be happy that you did.