Investigators want to question 35-year-old Oscar Ruiz about the attempted rape in Fort Tryon Park, in Washington Heights on Friday.
The mother fought off her attacker with a bike pump.
It happened just after 9 a.m. on a bike path in Fort Tryon Park, on the Henry Hudson Parkway near Dyckman Street.
The suspect approached the woman, who was pushing her 8-month-old baby in a stroller, with a broken bottle and grabbed her in a bear hug but she fought back, hitting him several times with an air pump, that she carries for the wheels on the baby stroller, causing a gash in the suspect's head.
"I had an extendable bike pump and I hit him. He got me in a bear hug and took me to the ground and I kept hitting up to his head cause he was behind me," said Mary Jane Jarman.
He fled, apparently losing his hat and sunglasses along the way. Police have recovered those items.
The woman refused medical attention and was not seriously injured.
"I just kept going. Nothing was going through my head except hit him hit him hit him," adds Jarman.
The stroller was knocked over in the struggle, but the baby was not hurt.
Jarman adds, ""I was protecting him for sure. I was not going to go down like that. I was protecting him with my life. I was prepared to kill this man."
The victim says at one point during the attack, the suspect said to her "I'm sorry, I'm sick."