Some police agencies require officers who use force to perform first aid to injured suspects. For instance, the Police Department in Greenville, N.C., has a policy stating that “the involved officer will render first aid to the individual until the arrival of E.M.S. unit.” But many departments do not explicitly require first aid, and officers follow more general protocols by simply ensuring paramedics arrive.

The Houston officers seen in the video work for the Precinct 4 constable’s office. Its top official, Constable Mark Herman, did not respond to requests for comment. At the time of the shooting, the department was led by Ron Hickman, who has since been appointed the Harris County sheriff. A spokesman for Sheriff Hickman referred questions to Constable Herman.

In Texas, constables and their deputies are state-licensed officers who perform duties similar to those of police officers, but who also serve eviction notices. It was unclear if the actions of the officers were being investigated by prosecutors. A spokesman for the Harris County district attorney, Jeff McShan, said the office does not disclose “what we are or are not investigating.”

A spokesman for the ambulance service, Cypress Creek E.M.S., declined to comment. Its response time of 10 minutes did not exceed the median response time for Harris County, which is 12 minutes. However, the overall delay of more than an hour in getting Mr. Goodridge to the hospital was called excessive by experts. Several factors contributed to the length of time, including a 30-mile trip to Ben Taub Hospital in Houston. In addition, dispatchers in the constable’s office initially contacted an ambulance service that did not serve that area. and then sent Cypress Creek E.M.S. to the wrong address, according to audio recordings of dispatch communications.

The officers appeared to be unaware of the problems getting an ambulance to the scene and put the responsibility of tending to Mr. Goodridge’s injuries on the paramedics, according to the dispatch communications. During the wait for the ambulance, the two officers seen most prominently in the video — Sgt. John M. Walton, who is white, and Deputy Constable Andres Rosas, who is Hispanic — asked dispatchers if paramedics were on their way and urged them to get E.M.S. there. Sergeant Walton, whose patrol car supplied the video, was asked if deputies needed additional assistance, but he told dispatchers that they did not.

“All we need to do is get this guy on an ambulance,” he added in the audio recordings.

Dr. Michael M. Baden, a forensic pathologist and the former chief medical examiner for New York City, reviewed the autopsy report and said that Mr. Goodridge could have survived if he had arrived at the hospital sooner.