The first thing to look at is the lease agreement. Sometimes it lays out responsibility for pest control. If you can't find information there, it likely depends on when the mice appeared. If they were there before the tenant, the landlord would have to take care of it. If they showed up after the tenant moved in, the tenant probably has to take care of it on their own. Regardless of who takes care of the problem, you should definitely look into this kind of thing seriously, and get the best help you can find to resolve the issue.
Many of the clients with PML of Longmont find it important to have specifics set out. You may want to have a lawyer review the lease.
With rents headed higher and vacancy rates in the single digits, people are doubling up. This can present problems for owners if additional people are not in the lease. You may even run afoul of HOA covenants and restrictions.
Make sure you have a well-written lease. A lawyer is your best bet if you're not working with a property management company.