It was late on March 3 when Daisha Smalls stopped at a Chevron station in Houston to pump gas.
Her 1-year-old son, Legend, was buckled in his car seat in the back, and Ms. Smalls said she was in the front seat when a man wielding a gun suddenly ran up to the car and demanded that she get out.
Ms. Smalls, 19, screamed at him that her baby was still in the back.
She said she could see police cars and hear sirens. Then she heard gunshots.
The gunman was dead. But the police had also shot her son in the head, the Houston Police Department said later.
As of Thursday, Legend remained in critical condition in pediatric intensive care, recovering from surgery to remove the bullet that had struck him.
“My son has been fighting every day for his life and he’s struggling on his own to breathe,” Ms. Smalls said during a news conference on Tuesday with her lawyers. “My baby didn’t deserve this. My baby didn’t deserve to be shot.”
The Harris County District Attorney’s Office, the Police Department’s internal affairs unit and the special investigations unit, an arm of the department’s homicide division, are investigating the shooting, said Jodi Silva, a police spokeswoman.
Only one officer fired his weapon, Ms. Silva said. The police have identified him by his first initial and last name as E. Garza. He is 38 and was sworn in as an officer in July 2006, Ms. Silva said.
He has been placed on paid administrative duty, she said.
Troy Finner, the executive assistant chief of the police, told reporters on the night of the shooting that he had spoken to the officer.
“We’re all praying for that baby,” he said. “He’s deeply concerned and hurting about this baby.”
Chief Finner said that the officer and his partner had gone to the scene that night “to protect lives, not to hurt anybody. And that’s tough on him right now.”
Chief Finner said he believed the officer did not know there was a child in the car.
The gunman was identified as Broderick Woods, 33, by the Harris County Institute of Forensic Sciences. He was a suspect in several “aggravated robberies,” the police said in a statement.
Officers tried to pull him over that night when they found him driving a black Mercedes-Benz. The suspect drove off and the police pursued him, leading to a chase that ended when the man lost control of the car and crashed it at the gas station. The officers then saw him running to Ms. Smalls’s car, according to a statement by the police.
The officers surrounded Ms. Smalls’s car and ordered Mr. Woods to drop his gun and show his hands. He refused, the police said.
Art Acevedo, the chief of police for the department, said in a statement on Tuesday that the officer fired his gun because he feared for the “mother’s safety.”
The police administered first aid to the baby and Mr. Woods, the police said.
Douglas Griffith, the president of the Houston Police Officers’ Union, said the officer did not know that there was a child in the car when he opened fire. He said the officers who were present at the time and who have reviewed body camera footage said it was clear the police pulled Ms. Smalls from the car before the shooting began.
“The officers that night worked with the information that they had at the time,” Officer Griffith said. “They engaged a violent suspect not knowing there was a child in the back seat.”
Officer Griffith added, “This entire incident took between three and five seconds.”
Ms. Smalls’s lawyers said they expected to file a lawsuit but were still gathering information about what happened. They disputed the police accounts that Ms. Smalls was out of the car when the shooting began.
“Were the actions of the Houston Police Department both objective and reasonable under the circumstances?” Antonio M. Romanucci, a lawyer for Ms. Smalls, said at the news conference. “Clearly the answer is no.”
Every day, Ms. Smalls asks doctors about her son’s prognosis, said Ben Crump, another one of her lawyers.
“‘Wait and see,’” they reply, according to Mr. Crump. “‘Hope for the best.’”
Ms. Smalls said she had not left her baby’s side since the shooting.
“I just want my baby to be safe,” she said. “I just want my baby to be healthy. I just want him to be back to how he used to be. I miss my son.”