According to court documents, Mohassib told investigators he went to the bike path carrying a knife because he believed "people were going to come and kill his family."
The criminal complaint further alleges that he later told detectives he disposed of the knife and bloody clothing and attempted to clean blood from inside his apartment.
Prosecutors allege surveillance video captured Mohassib walking toward the running path before the attack and running away from the area afterward.
Court documents also allege video showed him returning to his residence and later discarding items in a garbage chute.
Court records state that Katie Suarez went for a run along the path and never returned home.
The Office of the Chief Medical Examiner determined the cause of death was a stab wound to the neck.
The complaint alleges investigators found what appeared to be blood inside Mohassib's apartment, and a crime scene detective determined the stain tested presumptively positive for blood.
Mohassib was employed as a school aide with the New York City Department of Education at the time of his arrest.
He remains in custody pending further court proceedings.