"I'm innocent," Gonzalez said previously. "I didn't do nothing."
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The 25-year-old already had a lengthy police record before he was charged with running down FDNY EMT Yadira Arroyo last Thursday.
"It's hard, the fact that I am trying to get him to become a working person and try to straighten himself out," dad Jose Gonzalez, Sr., said.
Gonzalez, Jr., has 31 prior arrests, including criminal mischief, assault, marijuana sale and possession, turnstile jumping and public lewdness, and Eyewitness News has learned he has six prior interactions with police as an emotionally-disturbed person.
Most recently, he was arrested on February 25 for allegedly resisting arrest and kicking out a window in a police van. Prior to that, he was arrested last June for assault and harassment and reportedly released without bail in both cases.
Betsey Nevins-Saunders is assistant clinical professor of law and attorney-in-charge at Hoftra's Criminal Justice Clinic.
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"What the law is, it requires the court to set any conditions or restrictions that it must, in order to ensure the persons return to court," she said.
The law, she said, does allow the court to look at other factors in considering bail.
"The potential sentence they may be facing, so in that way, the court can consider priors and therefore potentially be thinking about danger," she said. "And it's always on the mind of the judge."
Gonzalez, Jr., is now being held without bail after being charged with two counts of murder in Arroyo's death.
"If anything, we used to always think something was going to happen to him because of the way he carries himself," Jose Gonzalez, Sr., said. "I never expected him to do something like this at all."
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Alice Fontiere, the suspect's attorney, said at his arraignment that Gonzalez, Jr., is severely mentally ill.
"In a murder case, that is a case where you are going to be thinking about a mental health defense," Nevins-Saunders said. "Whether it's an insanity route or a diminished capacity route."
So far, there has only be a request for Gonzalez, Jr., to receive medical attention.
Arroyo was a 14-year veteran of the force and a mother of five. She was assigned to Station 26 in the Bronx.
Her wake will be held on Thursday and Friday in the Bronx. Her funeral is scheduled for Saturday, also in the Bronx.
RELATED: Wake, Funeral arrangements for Yadira Arroyo