Police response to escape of a mental patient

I'm writing a story where a psychiatric patient slips out of sight of the orderlies accompanying the group during a supervised trip in the city. The patient in question is highly delusional, and though he's calm and easygoing enough when on his medication, he could become dangerous without them, especially in an unstructured environment.

The patient has been in a closed institution since he was twelve after shooting his father. Before that he was trained to shoot guns, use knives and other weapons and had some training in hand to hand due to said previously mentioned father, who was a former marine suffering from PTSD who pulled his two children on the road, forcing them in his own delusions along with heavy mental, physical and sexual abuse of his oldest, aka the patient in question.

My question then is, with this kind of patient, how long would it take before the police gets involved in the search and how big of a response would there be? And what would it take for the FBI to be called in?

And if said patient then ends up kidnapping a child, believing the boy to be his little brother, how would this affect the case. Especially if he takes the boy in question across state lines.



I looked in google under:
-police escape of mental patient Nevada
-treatment of mental patients by police officers

And I also asked on ask_a_cop, but haven't had an answer yet.