Mr Hale apologised to Mr Neely for the “unnecessary embarrassment”.
He added the officers “could have waited for a transport unit at the location of the arrest”.
“We have immediately changed the policy to prevent the use of this technique and will review all mounted training and procedures for more appropriate methods,” the police chief said.
Mr Neely is free on bond but could not be reached for comment, the Houston Chronicle reported.
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Leon Phillips, director of the Galveston County Coalition for Justice, told the BBC the image that went viral on social media was taken by an individual who wished to remain anonymous.
Mr Phillips said the incident is “difficult to talk about” as a Galveston resident.
“This was a stupid mistake,” he said. “What I do know is that if it was a white man, there’s no way they would have done that to him.”
He noted that Mr Neely is a mentally ill individual, and officers should have waited regardless of how long it took a vehicle to arrive, since “it’s not as if they’re getting paid by the arrest”.
Mr Phillips said he plans to file an open records request at city hall this morning to look at law enforcement policies.
“The police chief says they didn’t break any policy, but what is the policy on transporting a prisoner?
“How do I know that the policy wasn’t written in 1875? There are a lot of unanswered questions.”