Fort Bend County Sheriff's Capt. James Burger said the body of Engram Lamar Crenshaw, 37, of Katy, was discovered on Sunday morning, following a party at Smith's ranch-style home in a suburb about 30 miles southwest of the city.
Burger said Crenshaw was a personal friend of Smith.
Police and paramedics were called to Smith's home about 9:30 a.m. and found a fully-clothed man at the bottom of the pool. Burger said a preliminary examination of the body showed no signs of foul play, but he also said authorities were still piecing together the specific details of his death.
"He was not dressed to be swimming in the pool, I can say that," Burger said.
An autopsy will be performed on Monday in Galveston County. Burger expects results from toxicology tests to come back in about three weeks.
Burger said about 100 people, including "4 or 5" other Texans players, attended Smith's party on Saturday night. Burger said no Houston coaches or other staff members were there.
Witnesses told police that Crenshaw was last seen by party guests near the pool about 2 a.m.
"Apparently, he stayed out there by himself," Burger said. "In the morning, when people woke up and went outside, they discovered him in the pool."
The Texans open the regular season against Indianapolis on Sunday.
"We are aware of the situation," general manager Rick Smith said in a statement Sunday. "We are gathering facts and have no further comment at this time."
The 6-foot-4, 295-pound Smith is about to start his eighth season, and third with the Texans. He's started 31 of 32 games for Houston since signing with the team as a free agent before the 2009 season. Smith was originally a fifth-round pick by Arizona in the 2004 draft out of Oklahoma State.
Burger said no charges have been filed in Crenshaw's death.
"It doesn't appear that there's been any crime here," Burger said.