A 16 year old girl (17 in less than a month), has moved in with my family and I. She had no where else to go. Her father will not allow her to live at home and her mother lives in another state. Her mother has sent us a letter acknowledging her daughter living with us.
Is there anything else my husband and I need to do in order to legally have her or to not get in any kind of trouble for allowing her to live with us? We didn't even know who to contact to make sure we are doing our part in this.

Thank You

What state is each parent in? What state is the parent with court ordered custody in, if there is one? Where was their daughter living before she came to you?
Usually a letter from a parent isn't enough, but possibly when she turns 17 depending on the state she is supposed to be in.

It's a good thing that you have the letter from the mother in case any questions come up (to prove you haven't kidnapped the child, for example). But keep in mind that the letter does not make you the child's guardian - and therefore you have no authority to make decisions regarding the child's welfare such as enrolling her in school, attending teacher's conferences, consulting with doctors, or making decisions about her medical care, etc. So as long as either the mother or father is available and willing to accept responsibility as the child's parent, it's OK that the child is actually living with you.

Her mother lives out of state. The 16 year old is in California and has been. Her father is here in California and who she was living with last year. He is not responding to his daughters phone calls and has told her she cannot live at home.
When she is 17 does that change anything?
My husband wanted the letter in case dad gets crazy and claims we kidnapped her. We want to do whatever we need to in order to care for her.

Age of majority is 18 in California, so she can't make decisions on her own as to where to live until then.

In CA it's possible for you to go to court to have yourself appointed as guardian of the child's person, which generally requires that both parents indicate they are not willing or able to care for the child and request that you to be named as guardian. If this is something you want to pursue you should talk to an atttorney who specializes in family law to see if it's realistic or not.

But why is that the child can't live with her mother? You say the mother is out of state - but certainly the child can move out of state as well.

CA requires high school until 18 if not graduated. Is she in her father's same school system?
Emancipation law in CA starts at 14, but is difficult to get, and she must be supporting herself.
I would call your county courthouse Family Court to start, just to get general information. Don't worry about them coming after you or her.
I have a niece who finished high school in CA while living with an older brother, coming from CO, with various forms filled out for school and other responsibilities.

She could go with her mother on east coast but mom hasn't sent for her and its not a good environment. Father is who is suppose to have daughter but its not safe and dad doesn't care. I just want what's best for her. Thanks for all the info.

Just remember she is not legally with you, You have no right to give her medical care, can not legally enroll her in school. Nothing.
From a legal standpoint social services or CPS should be notified and be the ones to provide care for the child. You are open for possible legal issues just keeping the child.