You'd definitely find dry little black rice-grain-like droppings on all surfaces if you had mice, especially in rooms that have food, and more will appear if you clean them away. Also, little sticky splotches that are easy to mistake for drink spillages, because they pee everywhere too.

I managed to get rid of mine, but I occasionally still find evidence they were here in out of the way corners that I forgot about.

Brave mice - because I'm sure some will have that trait - and those infected with toxoplasmosis won't care about cats.

Good luck.