There is a lot that could be going on here..... you said she lives with mom only. Have the parents recently (and I mean in the last year or so) separated? That can really change a child's behaviour for quite a long time. Perhaps she is just a more reserved child. She just may not be a smiley and happy child. Sad, but that may be her personality.
I would probably approach mom, since it has been 3 months now (should be long enough to settle in/ adjust). Let her know that you have no issues with her behaviour, but that you want to make sure she is happy. Ask her about grandma's house. This little girl may just be super attached to her mommy, and missing her, especially if mom has just gone back to work full time recently or something like it.