Bats

We have had a bat house on our house for a couple of years, but the location didn't seem to be very good as it didn't attract any bats. Well, this summer, our big birch tree in our backyard 'mostly died', so we decided to cut off the branches but leave the trunk up so that we could move our bat box there. Well, I'm still not sure that any bats have moved in, but our cat decided to let us know that there are, indeed, bats in the area. Merlyn (our cat), is a very good hunter, catching things like mice, bugs, and birds (although I try to keep the bird hunting to a minimum by letting him out at night). I had never thought that he might catch something like a bat! The bat was still alive when we 'rescued' it from him and moved it to a tree (see picture). Unfortunately, it didn't survive the night. Does anyone know if the little brown bats here carry rabies, or if it is an issue? We have never gotten our cats vaccinated for rabies, but now I am wondering if I should!