The Texas Property Code requires the landlord to repair any problems that are a threat to the health or safety of an ordinary tenant. Mice would fall under that obligation from the landlord because they could carry diseases. A landlord cannot transfer that responsibility to the tenant. Courts have stated that such pest as rats, mice, raccoons and squirrels are the landlords responsibility under Texas Property Code as they can harbor diseases, fleas, rabies, etc. which all are considered health and safety issues.
Mice can cause considerable damage if not taken care of. So you need to verify that you either have a problem or not. Then if their is a problem, take care of it by hiring an extermination company.