A US mother who was allegedly shot dead by her 9-year-old adopted son feared she was raising "the next serial killer", her family have revealed.

Pauline Randol, 51, was shot dead at her Michigan home on Monday, with her young son charged with murder the following day.

The victim's daughter said her brother was adopted three years ago and had a history of mental health issues, saying he "just recently started snapping", terrifying their mother.

The family say Randol had booked an appointment with mental health care officials for the Tuesday after she had concerns over his deteriorating mental state.

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But the day before the appointment, Randol was found dead after being shot with a rifle in her own home.

"She had told her doctor one time she was so scared she was raising the next serial killer," daughter Harley Martin told 24 Hour News 8.

Another daughter told the Detroit News that Randol had been desperately trying to get more mental health help for the boy.

"She eventually got an appointment … but that was supposed to be for Tuesday, and it was too late," said Reagan Martin.

"My mother's death lays in the hands of people failing to educate in mental issues and failing to listen when helped is being begged for."

"She had told her doctor one time she was so scared she was raising the next serial killer."

Pauline Randol took the boy in when he had nowhere else to go. Photo / Facebook
Pauline Randol took the boy in when he had nowhere else to go. Photo / Facebook

The boy was charged with murder, and using a firearm during the commission of a felony.

It isn't clear if he was charged as an adult or a juvenile. Authorities have not released the circumstances of the killing or details of why the child was charged.

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Martin called her adopted brother "a sweet, caring young man who needed help further than the help my mother gave him, and she tried".

The child is undergoing a psychiatric evaluation at a state-run juvenile facility, according to St Joseph County Sheriff Bradley Balk.