Video of the incident has stirred debate about what type of force police should have used to detain a man with a gun.
"Everything in the video seems to point towards an obvious excessive use of force. It is miraculous that my client isn't dead," said attorney Michelle Cohen-Metzger.
The incident was recorded February 19 on the dashcam of two Marana police cars that were following the suspect, 36-year-old Mario Valencia.
In one video, an officer who was tailing Valencia at slow speed reports over the radio that the suspect has fired one round in the air with a rifle he is accused of stealing that morning from a Walmart.
Another patrol car zooms past, runs into the man from behind then hits a short cinder block wall next to a driveway. Video from Officer Michael Rapiejko's camera shows the officer running the man over and the windshield smashing as the car hits the wall.
"Oh Jesus Christ. Man down," the officer in the first car says.
Police in Marana, which is about a half-hour from Tucson, have justified Rapiejko's actions.
"If we're going to choose between maybe we'll let him go a little bit farther and see what happens, or we're going to take him out now and eliminate any opportunity he has to hurt somebody, you're going to err on the side of, in favor of the innocent people," Police Chief Terry Rozema said. "Without a doubt."
The situation warranted deadly force because the suspect was headed to an area where several hundred people were working, Rozema told CNN's Brooke Baldwin.
"This officer made a split-second decision, and in retrospect, when all the dust clears, I think we look at this and say, yeah, there's things we can learn from this," he said, "but the entire community is safe, all the officers are safe, and even the suspect in this case is safe."
Cohen-Metzger said officers didn't make any effort to de-escalate the situation of a man "clearly suicidal, clearly in crisis."
CNN affiliate KOLD
reported Valencia was in serious condition when he was taken to the hospital and was released into police custody two days later.
Timeline of events
Tucson Police Sgt. Pete Dugan told CNN that Valencia was involved in several incidents in Tucson the day he was struck.
At 6:45 a.m., Valencia robbed a 7-Eleven in Tucson with a metal object in his hand. Authorities said he was dressed only in his underwear. He was charged with theft.
A little more than an hour later, police said, Valencia set a fire at a church for which he was charged with arson of an occupied structure.
Just after that he entered a home and stole a car, police said.
Authorities said he drove to a Walmart where he stole a .30-30 rifle and ammunition. He fled the store with Walmart employees in pursuit.
Police encountered him in a business park walking down the road. An officer told him several times to drop the rifle, Lt. Tim Brunenkant with the Marana Police Department said in an email containing a timeline of events.
Valencia, police said, walked away from the officer, turned a corner and stopped. Valencia pointed the rifle at the officer then walked away again toward a Coca-Cola bottling plant and another business.
"As Mario Valencia briskly walked towards Sargent Controls (local manufacturer), Officer Michael Rapiejko uses his marked police car to stop the dangerous situation Mario Valencia created," Brunenkant wrote.
Brunenkant also said by phone that before Rapiejko's encounter with Valencia, the suspect had pointed the rifle at his head multiple times and threatened suicide before fleeing.
Cohen-Metzger criticized the fact that Rapiejko hit Valencia from behind.
"My client's back was turned and the officer drove right into him," she said. "It isn't that dissimilar to a police officer shooting a fleeing suspect in the back."
But Harry Houck, a former New York Police Department detective, said it was the right move.
"What if that (suspect) walks into somebody, maybe taking a potential hostage, maybe just shooting somebody," he told CNN's "Anderson Cooper 360˚."
After a man fires a gun in the air, officers have to make a decision how to detain the man, Houck said. Do they surround him with their cars and get in a gunbattle? That would risk the lives of officers and bystanders, he said.
"I'm 100% behind this officer," Houck said.
Dan Bongino, a former Secret Service agent, told Cooper the suspect had to be stopped but not with a vehicle running into him.
"I have to question this tactic a bit," he said. "I think setting up a secure perimeter and at least making some attempt to negotiate may have been far more efficient."
Houck insisted the officer likely saved lives.
Host of charges
Valencia faces 15 charges, including three counts of aggravated assault, three counts of armed robbery and possession of a deadly weapon by a prohibited possessor. Cohen-Metzger said he had a prior record.
His next court appearance is May 18. He is in the Pima County Jail.
Authorities said no charges have been brought against the officer.