Britt Reid, the outside linebackers coach for the Kansas City Chiefs and a son of the head coach, Andy Reid, told police officers he had “two or three drinks” before he was involved in an automobile crash Thursday night that left a child with life-threatening injuries, according to a search warrant filed in Jackson County, Mo., circuit court.

The crash occurred just days before the Super Bowl in Tampa, Fla., on Sunday, when the Chiefs, the reigning N.F.L. champions, played the Tampa Bay Buccaneers. The Chiefs flew to Tampa on Saturday, but Britt Reid, 35, did not make the trip.

According to the search warrant, an officer could smell “a moderate odor of alcoholic beverages” on Reid after the crash. The search warrant said the police sought to draw Reid’s blood and test it for alcohol and other controlled substances.

On Friday, in a statement, the team confirmed that Reid had been involved in a crash, but provided no details. “We are in the process of gathering information, and we will have no further comment at this time,” the statement said.

In response to an inquiry about a possible car crash involving Britt Reid, a spokesman for the police department in Kansas City, Mo., said that a crash had occurred on Interstate 435, not far from the Chiefs’ training facility.

The spokesman would not provide more details or identify anyone who was involved in the crash, citing a Missouri law that prohibits the police from releasing the names of people who have not been charged with a crime. But the details in the police incident report, such as the make and model of the cars involved and the description of what happened, matched the search warrant, which does name Reid.

According to the police, a vehicle ran out of gas on a freeway entrance ramp less than a mile from Arrowhead Stadium. The driver stopped with his flashers on and called his cousins for help. When they arrived, the cousins parked in front of the disabled car and left their lights on, as the battery was dying in the disabled car.

Reid entered the on-ramp driving a Ram pickup truck and hit the left front of the stranded car, according to the police incident report. The driver was sitting in the car and was not injured.

Reid’s pickup then slammed into the rear of the cousins’ car. The driver and an adult in the front passenger seat were not injured. But a 4-year-old and a 5-year-old sitting in the back were both injured and taken to the hospital, the 5-year-old with life-threatening injuries.

The 5-year-old was still in critical condition on Monday morning with a brain injury, according to a police statement.

After the Super Bowl, which the Chiefs lost, 31-9, Andy Reid addressed his son’s car crash for the first time.

“My heart goes out to all those that were involved in the accident, in particular the family with the little girl who’s fighting for her life,” Andy Reid said, adding that his “heart bleeds.”

Britt Reid had non-life-threatening injuries, the police said, but complained of stomach pain and was also taken to a hospital after the crash.

“Most serious-injury/fatality crashes take weeks to investigate, as do criminal investigations,” the Kansas City Police Department said in a statement released Monday, explaining why no arrests have been made and the names of those involved in the crash have not been released. “This is no different.”

Reid has been a Chiefs coach since his father was hired as head coach eight years ago, and has spent the last two seasons as the outside linebackers coach. Before joining the Chiefs’ coaching staff, he spent three seasons at Temple University as a graduate assistant working with the offense.

He was also an intern for his father with the Philadelphia Eagles in 2009.

Britt Reid has been in legal trouble previously. In 2007, Reid, then 22, pleaded guilty to gun and drug charges stemming from a road rage dispute. He brandished a handgun at another driver in suburban Philadelphia on the same day his brother Garrett was arrested after a drug-related traffic crash. Andy Reid took a five-week leave of absence from the Eagles after his sons were arrested.

Britt Reid also pleaded guilty to simple assault, possession of an instrument of crime and drug possession in the case. While out on bail before the case was decided, he was arrested after driving into a shopping cart in a parking lot and eventually pleaded guilty to driving under the influence.

In 2012, Garrett Reid was found dead of an accidental overdose in his dormitory room at the Eagles’ training site in Bethlehem, Pa. He was 29.