I own a fourplex and live in one of the units.  Recently I found some signs of mice.  I have laid traps and caught a few.  I live above an tenant who has lived there since I bought the property.  Her apartment is cluttered to say the least, but besides that she is a good tenant. She's quiet, pays on time, etc.  I haven't heard from her or any other tenant with issues of mice.  I am unsure how to proceed.  I don't want to cause worry with the other tenants, but I don't want to be a scummy landlord and pretend this isn't happening.  I also feel like as long as the tenant is there this issue will linger.   
Has anyone gone through this or have any suggestions? 

Thank you. 

@Joe K. Are you inspecting every 6 months? If you are not I would recommend you start. If you are look for signs of mice in the other units. It is highly unlikely the mice are just in your unit.