The symptoms you are discribing sound very much like our 4 yr. old son. His preschool teachers thought he might be on the autism spectrum, and we immediately follwed-up with our doctor. He has been evaluated by several professionals , and nobody has placed him on the spectrum at this time. However, we are continuing to monitor his behavior for the next year to see how he progresses socially.
The mimicking that you spoke of sounds very much like echolalia. It is a symptom of ASD and should be watched closely. Our son was displaying some echolalia behaviors, that seem to be waing now, but were very concerned for a while. Does this child also repeat phrases from movies or books over and over again? Does she often repeat the last few words spoken to her over and over in a rhythmic pattern? If so, I would suggest you look up echolalia and mention it to her parents. And I would absolutely pursue these issues with her parents. In the case of our son, he was a totally different child at school than at home. He became very social and interactive at home, but would shut down at school. This may be the case with this child as well. Good Luck!
how long has she been in preschool? My son is 3 and 1/2 and he did that too when he first started preschool/daycare. For about the first month maybe a little longer I'd say, he would not stop mimicking other kids. The teachers finally commented on this and we'd talked to him. He seems to do it now when he's around kids or people he's not really familiar with. Then once he gets comfortable he's himself again. Now when he does it, its because he knows it irritates them.
The behavior is not normal, as you have indicated. I think that the child should be evaluated by a professional to determine what in her social skill development she is "missing" and why she is connecting in this way.
As I am sure you are aware, "missing" social cues can be indicative of various issues--some of them quite serious -- and it can be very damaging to children as they are growing up. When kids are young, they generally don't get teased or left out-- but not so when they are the "odd" kid in the 4th grade.
You could try to talk to a professional and/or someone with experience in social skills training for children this young to get some ideas of what you might be able to do in your classroom to help her with her social development. However, her parents really have to take the full action to get her evaluated so that they can help their daughter-- as her teacher, you can't help her nearly as much as they can.
It sounds like the parents may not realize how serious the situation is-- and I understand how this can be a very touchy subject with parents. What you might want to do is to indicate to the parents that you are going to seek out some advice on what you can do in your classroom to try to help her with her social skills development. It could be that hearing that you are seeking additional help for her, because its not in the realm of normal behavior and you are concerned, may give them the wake up call that they need -- in a completely non confrontational manner-- that their daughter is in need of some help.
I have talked with the parents many times they reply with "yeah I know she's annoying". I was just looking for someway I can help her, she does not do well with being distracted for example if I tell her lets paint or play dress up she starts to cry and just shuts down. I would love to understand why she behaves like this and what I can do on my part to help her become more independent without being overbearing.
Have you told the parents this? Most children at age three will stop a behavior if told that it annoys someone else. Your best asset is their short attention span. I would distract her to something else.
Good luck and God bless.