Burress shot himself in the right thigh at a Manhattan nightclub over the weekend in a case that has angered the mayor of New York.
Police were searching for more answers from teammate Antonio Pierce and the hospital that treated Burress. Pierce was with Burress at the nightclub, and police want to know what the linebacker did moments after the shooting and whether he helped cover up what happened.
Police expressed frustration with the NFL and Giants officials, saying they were promised that Pierce would appear Monday at a police precinct where Burress appeared before heading to court. But he didn't show.
"It was a universe of silence after this shooting," New York Police Department spokesman Paul Browne said.
The hospital that treated Burress has come under scrutiny. New York-Presbyterian Hospital/Weill Cornell Medical Center said officials "take this very seriously, and are conducting a thorough investigation into why this gunshot wound was not reported to the police department in a timely fashion."
Myrna A. Manners, the hospital's vice president for public affairs, told The New York Times that a person responsible for not reporting the gunshot wound had been suspended.
The developments came just 10 months after Burress made the winning catch in the Super Bowl. But on Monday, Burress was hauled out of a police precinct in handcuffs facing two weapons charges.
Burress posted $100,000 bail and was told by the judge that his next appearance won't be until March 31. In the meantime, the Giants and the NFL will have to make a decision about what to do with the troublesome wide receiver.
The 31-year-old player did not say anything in court Monday and did not make a statement to police when booked at a midtown precinct. His lawyer stressed that Burress is innocent until proven guilty and denied Burress took part in any cover-up.
"He is standing tall. He is a mature adult," said Benjamin Brafman, his defense lawyer. "I think any professional athlete in this situation would be concerned."
The case drew the wrath of Mayor Michael Bloomberg, who said it would be an outrage "if we didn't prosecute to the fullest extent of the law" and lashed out at the hospital for allegedly failing to report the shooting to the authorities.
Burress shot himself in the right thigh in the VIP section of the Latin Quarter nightclub about 1 a.m. Saturday, police said. He did not have a permit to carry a handgun in New York.
A witness reported hearing a popping sound before Burress' legs began to shake, according to a criminal complaint. It said the person saw a bloody pistol fall out of his pant leg and land on the floor before Burress said, "Take me to a hospital."
Burress was charged with two counts of second-degree criminal possession of a weapon, which could result in a prison sentence of 3½ years to 15 years if he is convicted.
Originally, police said that running back Derrick Ward was with Burress and Pierce at the club, relying on information given to them from security guards at the club. But police said later it was unclear if Ward was at the club, and the running back strongly denied he was.
Police said that the Giants have sent a member of their medical staff to the precinct who may be able to shed some light on what transpired the night of the shooting, and presumably to relay Pierce's version of events.
Pierce declined to provide specifics about the incident Monday during a radio interview, but said that many facts of the case have been "misconstrued" and "distorted." He said he has hired an attorney but that he doesn't see himself being arrested.
"Today has been a headache and that's about all I can say," he told WFAN.
The Giants released a statement disputing the police's version of their involvement.
"We are working closely with the police and NFL Security," it said. "In the early hours of Saturday morning, as we started to get a sense of what we were dealing with, we did, in fact, notify NFL Security, which then contacted the police."
The Giants have not decided what to do with Burress, who was suspended for a game and fined for missing a team meeting in September. New York could suspend him again or deactivate him for Sunday's home game against the Eagles. The Giants could go as far as releasing Burress, but that would put a strain on the team's salary cap next season.
"We're dealing with that," coach Tom Coughlin said during a conference call Monday. "Today we had some discussions and those discussions will be ongoing."
Coughlin would not speculate on what the team would do if Burress showed for practice Wednesday.
NFL spokesman Greg Aiello also said in a statement the league was cooperating. "In addition, it will be reviewed under our league policies," he said.
Bloomberg has waged a long fight against illegal guns. He called for a full prosecution of state law that requires mandatory prison for carrying a loaded handgun. He also criticized the hospital, based on the allegation that officials may not have properly reported the shooting.
"It's just an outrage that the hospital didn't do what they were legally required to do," he said.
Associated Press Writers Colleen Long, Samuel Maull and Tom Hays in New York, and AP Football Writer Dave Goldberg contributed to this report.