"Pioli and Crennel and another coach or employee was standing outside and appeared to be talking to him," Snapp said. "The suspect began to walk in the opposite direction of the coaches and the officers and that's when they heard the gunshot. It appears he took his own life."
The coaches told police they never felt in any danger.
"They said the player was actually thanking them for everything they'd done for him," Snapp said. "He was thanking them and everything. That's when he walked away and shot himself."
Members of the Chiefs mostly laid low Saturday, but a few reacted on Twitter.
"I am devastated by this mornings events," Pro Bowl linebacker Tamba Hali wrote. "I want to send my thoughts and prayers out to everyone effected by this tragedy."
A large group of Belcher's friends and relatives gathered Saturday at his boyhood home on Long Island.
His family turned the front yard into a shrine, with a large poster of Belcher, an array of his trophies, and jerseys and jackets from Kansas City, Maine and West Babylon High.
"He was a good, good person ... a family man. A loving guy," said family friend Ruben Marshall, who said he coached Belcher in youth football. "You couldn't be around a better person."
At least 20 people gathered for a large group hug in the driveway.
"He was a tremendous player and all those things, and his accolades speak for themselves, but he lit up when he spoke about his mom, or when he hugged his family after games," said Dwayne Wilmot, who was Belcher's position coach at Maine and is now an assistant coach at Yale.
"It's difficult to talk about Jovan in the past tense," he told the AP. "There's going to be unanswered questions, the why's of this tragedy. It'll never be truly known to us."
Wilmot said he'd stayed in touch with Belcher the past few years through social media.
"He was someone who took genuine pleasure in bringing happiness to others," Wilmot said. "I was so excited when he became a father, because I knew he'd be a great father."
His girlfriend's Facebook page shows the couple smiling and holding the baby.
Belcher is the latest among several players and NFL retirees to die from self-inflicted gunshot wounds during the past few years. The death of star linebacker Junior Seau, who shot himself in the chest in at his California home last May, sent shockwaves around the league.
Seau's family, like those of other suicide victims, donated his brain tissue to medical authorities to determine if head injuries he sustained playing football might be linked to his death. That report has not been released, although an autopsy showed no underlying hemorrhaging or bruises on Seau's brain.
Belcher did not have an extensive injury history, though he was listed as having a head injury on a report from Nov. 11, 2009. Belcher played four days later against the Oakland Raiders.
Earlier this year, the NFL provided a grant to help establish an independently operated phone service that connects players, coaches, team officials and other staff with counselors trained to work through personal and emotional crises. The NFL Life Line is available 24 hours a day.
The season has been a massive disappointment for the Chiefs, who were expected to contend for the AFC West title. They're 1-10 and mired in an eight-game skid marked by injuries, poor play and fan upheaval. During the past few weeks there have been constant calls for Pioli and Crennel to be fired.
It's unknown how the Chiefs plan to pay tribute to Belcher during Sunday's game.
"His move to the NFL was in keeping with his dreams," said Jack Cosgrove, who coached Belcher at Maine. "This is an indescribably horrible tragedy."
Associated Press Writers Heather Hollingsworth and Frank Eltman contributed to this report.
Online: http://pro32.ap.org and http://twitter.com/AP_NFL