I am considering putting some of my properties under property management. I have a question about leases. If my property manager is in charge of finding tenants and signing leases with them, what happens to those leases if the property manager should move out of town or close up shop? Do I need to sign new leases with the tenants? I am hoping that the rights and responsibilities under the lease revert to me. This would make the most sense to me, but I wanted to be sure. :)

The lease is between the landlord (you) and the tenant. Your property manager is simply acting as your agent (in the literal sense of the term).

Some PMs may sign the lease for you (if they have a power of attorney or their PM agreement permits them to do so). But they are signing for you. The tenant is still renting the property from you, not from the PM.

If you change property managers, it has no impact on your leases, other than maybe changing details such as how/where rent is paid. But that can be solved with a simple written notice, it does not require a new lease. 

Thank you Jeff, that is what I was hoping to hear.  :)