Documents obtained by CNN show that McKane was married Monday, a day after San Antonio police Detective Benjamin Marconi was shot dead.
McKane, 31, was arrested just hours after his marriage on suspicion of killing Marconi. Police say they believe Marconi was killed specifically because he was a law enforcement officer.
The name of the person McKane married was redacted in the documents CNN received. A marriage license was issued at the Bexar County Clerk's Office at 9:57 a.m. CT Monday, the documents show.
A judge then performed the ceremony, said Priscilla Hernandez of the Bexar County Clerk's Office.
Around that time, San Antonio police were publicizing surveillance video, recorded Sunday, of the man they believed shot Marconi, but did not release a name. The video showed a man seen inside police headquarters four hours before the shooting and a car leaving the scene, CNN affiliate KPRC reported
Marconi, 50, was shot at close range Sunday before noon as he wrote a traffic ticket outside of police headquarters.
Police arrested McKane late Monday afternoon. A SWAT team stopped him as he was riding with a woman and a 2-year-old child on Interstate 10, San Antonio Police Chief William McManus said.
McKane already has offered an apology to the dead officer's family. As he was being escorted out of the police department after his arrest, reporters asked him why he had been upset.
"Society not allowing me to see my son," McKane replied.
"I lashed out at somebody who didn't deserve it."
"I've been through several custody battles and I was upset at the situation I was in."
When asked if he had anything to say to Marconi's family, he replied: "I'm sorry," as he was escorted away.
Police say Marconi had pulled over a driver on the south side of the police station on Sunday and returned to his patrol car to write a ticket.
That's when a man pulled up behind him.
The man walked up to the patrol car driver's side window and shot the officer in the head, McManus said. The man then reached through the open window and shot him a second time, he said.
After the shooting, the man returned to his vehicle and drove away.
Officers found McKane by using videos and information turned up by the investigation, the chief said. They kept him under surveillance for several hours, police said. It wasn't immediately clear if that surveillance covered McKane's visit to the courthouse for the wedding.
"Based on the actions of this individual prior to the shooting, we have a fairly good video documentation of what he was doing," McManus said. "I am still convinced that he was targeting blue -- targeting a San Antonio Police Department officer, no matter who it was. It was any officer he came across."
"This case, although we've made an arrest, is far from over," McManus said.
"We continue to investigate and until we have every shred of evidence that we believe exists, we'll then turn it over to the District Attorney for prosecution."
McKane has a criminal history. In 2012 he pleaded no contest to an assault charge, according to a court database.
Several police officers targeted over weekend
The police shooting in San Antonio was one of four incidents in which law enforcement officers were shot Sunday.
Marconi was the only fatality that day, but his death marked the 60th fatal shooting of an officer in the line of duty this year
, according to the National Law Enforcement Officers Memorial Fund.
Well-wishers formed a makeshift memorial with flowers, balloons and cards in honor of Marconi in front of San Antonio police headquarters.
His family released a statement thanking the community for their support and prayers.
"He was well-respected," McManus said of the 20-year police veteran. "He was a great guy, a great investigator. He was just a solid guy and I can't describe the loss to the police department and the community."