An Ohio man drove his car into a sheriff’s deputy, killing him in what the authorities said appeared to be an intentional act that happened the day after the driver’s 18-year-old son had been shot and killed by the Cincinnati police.

The man, Rodney L. Hinton, 38, was being held without bond on Saturday on one count of aggravated murder, according to documents in Hamilton County Municipal Court.

Mr. Hinton is accused of hitting a Hamilton County deputy who was directing traffic outside of a University of Cincinnati graduation event at approximately 1 p.m. on Friday, Chief Teresa Theetge of the Cincinnati Police Department said at a news conference on Friday.

The chief said that “there is a connection” between the fatal crash and a shooting the previous day, though there was no indication that the driver knew the deputy. The deputy’s death followed the fatal shooting by a Cincinnati police officer of Mr. Hinton’s 18-year-old son, Ryan Hinton, during a pursuit on Thursday night, Chief Theetge said.

The deputy who was killed was not publicly identified by the authorities. The sheriff praised the deputy’s work with the department.

“He was so well-liked and so well-known, we could fill this building with the law enforcement agencies that respect him, love him,” Sheriff Charmaine McGuffey of Hamilton County said at the news conference. “I knew the man and I knew what a tremendous, tremendous person he is and what a tremendous loss we have all suffered.”

At a separate news conference on Friday morning, before the fatal crash, Chief Theetge said that city police officers responded to a residential cul-de-sac on Thursday, where they found a car that had been reported stolen in northern Kentucky.

Four people were inside the vehicle and they ran when officers approached. One of the four people, identified by the authorities as Ryan Hinton, had a gun in his hand, Chief Theetge said.

According to body-camera footage shown at the news conference, Ryan Hinton briefly fell on a sidewalk as he ran from an officer, at which point the officer called out that Mr. Hinton had a gun.

As the pursuit continued, Mr. Hinton ran between two dumpsters at the end of the cul-de-sac and another officer fired multiple times. Mr. Hinton fell to the ground and the responding officers provided first aid, Chief Theetge said. There was no indication that Mr. Hinton had fired his gun, she said.

A firearm was recovered at the scene, the chief added. Another gun was found inside the stolen car, the police said. The Cincinnati police officers involved in the episode have not been publicly identified.

The Hinton family had gathered around 10 a.m. on Friday at the Cincinnati police chief’s office to view body-camera footage from the shooting, according to Michael Wright, a lawyer retained by the Hinton family in the shooting case.

Mr. Wright, who was with the family at the chief’s office, said that Rodney Hinton was very upset and walked out before the video was over. The group left the chief’s office around 11 a.m., roughly two hours before the deputy was hit, said Mr. Wright, who is not representing Rodney Hinton.

“This is a horrible, horrific incident on both ends there,” Mr. Wright said, adding that the Hinton family was “sad for the family of the police officer” and “sad because of what happened to their son.”

Gov. Mike DeWine of Ohio said in a statement on Friday that he had been briefed on the investigation, adding that he was “sickened by what appears to be an intentional act of violence.”

Connie Pillich, the prosecuting attorney for Hamilton County, said on Saturday that “unfortunately, it appears that his father was extremely distraught and, for whatever reason, may have committed this horrible offense.”

Ms. Pillich described a community on edge following the two episodes, calling the city’s mood “very fragile.”

The shooting on Thursday was the fourth police-involved shooting in the county this year, and its second fatal one. The first three shootings were investigated and determined to be justified, Ms. Pillich said. Her office is investigating the latest one.

The prosecutor’s office has contacted faith leaders, asking them to encourage their congregants to “let the process work,” she said.