I do not think so; I am pretty sure you can have both. If you have clever mice that are mentioned in the post below then you will not have any pussy cats in your home:
Mice are afraid of rats. Rats are known to kill and eat mice. So if you have rats, you probably won't have mice. If you have mice, it just means there aren't any rats around.
Definitely not. We get both in our loft!! Living where we do in the type of house we live in, rats are a constant problem, especially in the winter when they come in off the fields. Mice also remain in the loft. I would add that although we get the odd mouse in the house, we have never had a rat, except in the loft.