Bail was set at $1.5 million Monday for a homeless man accused of attacking and sexually molesting an 83-year-old woman near 159th Street and Harlem Avenue last week.

Dennis D. Dodson Jr., 34, without a last known address, was charged with one count of aggravated criminal sexual assault, a Class X felony.

According to state prosecutors, Dodson was living in a forest behind a nearby Orland Park shopping mall when the elderly woman offered him crackers and $15 cash.

Two days later, she came back to tell Dodson that she had spoken with area police and firemen about local homeless shelters and found him surrounded by beer cans. Orland Park police say that’s when Dodson attacked her.

In court on Monday, state prosecutors described a struggle in which Dodson kissed and pulled the screaming woman to the ground, molesting her forcefully with his finger. She managed to escape on her bicycle after sustaining scratches and bruises all over her body, prosecutors said.

For Judge Peter Felice, prosecutors also ran through Dodson’s 16-year history of convictions and imprisonment that includes burglary in Iowa, disorderly conduct in New York and a stolen motorcycle in Ohio.

Dodson has a history of mental health issues and takes psychotropic medication, according to a public defender who asked that the court order psychological testing to gauge her defendant’s mental fitness.

Felice told Dodson’s attorney to take the issue up with the prison warden, saying, “I suspect (Dodson) may be feigning the issue.”