In most cases, yes.
Managing and handling production permits is almost always the responsibility of film crews. The host should also be knowledgeable if a permit is required for productions in their area/neighbourhood and be able to provide relevant information to the renter.
There are some American cities where hosts must register, get a permit, or obtain a license before they can list their property or accept commercial projects in their space. Certain types of bookings may be prohibited altogether. Municipal and county laws vary greatly, as does the process of enforcement.
If you have questions or concerns about the legality of hosting film shoots, please reach out to local authorities for correct and up-to-date information on permitting.