Officers were summoned to the American Airlines plane about 9:30 a.m. at Miami International Airport, according to the Miami-Dade Police Department.
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"The flight crew was concerned for a passenger (Mr. Odell Beckham), as they tried to wake him to fasten his seat belt, he appeared to be coming in and out of consciousness, prior to their departure," the Police Department said in a statement. "Fearing that Mr. Beckham was seriously ill, and that his condition would worsen through the expected five-hour flight, the attendants called for police and fire rescue."
When officers arrived, members of the flight crew asked Beckham "several times" to exit the plane but he refused, the news release said.
The aircraft was "deplaned," and when police asked Beckham to exit the aircraft he did so without incident, according to authorities.
Officers escorted the NFL wide receiver to the non-secure area of the airport terminal, where he made other arrangements for travel, police said. The flight took off almost two hours after initially scheduled.
Without specifically addressing the incident, Beckham tweeted on Sunday morning: "Never in my life have I experienced what just happened to me... I've seen it alll.."
He later tweeted: "I COULD NEVER MAKE THIS UP."
Authorities said Beckham was neither arrested or cited, according to NFL.com.
Beckham, who has not played this season while recovering from a torn ACL suffered in last season's Super Bowl, was expected to meet with teams this week ahead of a possible signing.
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The Dallas Cowboys are believed to be the front-runners to sign Beckham, with the Kansas City Chiefs, Buffalo Bills and San Francisco 49ers also in the mix.
ESPN contributed to this report.