Originally Published: 19 JUL 21 03:30 ET

Updated: 19 JUL 21 11:40 ET

By Joe Sutton, CNN

(CNN) -- Police in Tucson, Arizona, are investigating a deadly shooting rampage across three crime scenes, including a burning house where a charred body was found Sunday.

The 35-year-old male suspect, whom police have not identified, was in "very critical condition" after exchanging fire with police, Tucson Police Chief Chris Magnus said at a Sunday evening news conference. Police believe only one suspect was involved in the complex incident, he said.

The rampage began Sunday afternoon at a park, not far from a residence that police believe was set alight by the suspect, Magnus said.

After flagging down two EMTs at the park and pointing in the direction of the fire, the suspect opened fire, striking a 20-year-old EMT driver in the head and a 21-year-old EMT worker in the arm and chest, according to a statement from the Tucson Police Department.

The EMT driver was in critical condition and the second EMT worker was in a stable condition, Magnus said Sunday evening.

While the park shooting was unfolding, fire department personnel and some neighbors were trying to extinguish the nearby house fire. Children linked to the residence later were located and accounted for, Tucson Police Sgt. Richard Gradillas told CNN on Monday morning. H would not give the number of children or their ages.

Burning residence and gunfire exchanged

As the home continued to burn Sunday, the 35-year-old male suspect arrived at that site and opened fire, Magnus said.

A 44-year-old neighbor was shot in the head and killed, the chief said. A Tucson Fire Department captain of 17 years of service was hit in the arm and was in stable condition, while a second neighbor was grazed in the head by a bullet and was in a good condition, he said.

A badly burned body was found inside the home, Magnus said. Authorities could not immediately establish its gender or relationship to the suspect.

Police responded after fire personnel had notified them that they were being shot at as they fought the blaze, Magnus said. Then after the suspect fled the scene and was spotted by police, an officer-involved shooting occurred at a third location.

The officer and the suspect saw each other, and the suspect rammed the officer's patrol car, disabling it, Magnus said. The officer got out of the car when the suspect began shooting and returned fire, striking the suspect, Magnus said.

The officer who exchanged gunfire with the suspect is an eight-year veteran of the force, the chief said.

"This is both a highly tragic, really horrific incident with many unknowns at this time," Magnus said at the news conference.

The investigation is ongoing.