Air Force veteran Edward "Dread" Smith, arrested in 2008, is one of them.
Smith said his electric wheelchair, which the VA supplied, malfunctioned and hit a pillar at the Uptown Division in 2007. The charging document said he "willfully and unlawfully" caused the damage.
Besides two counts of damaging government property, he was charged with simple assault after being accused of running over a man's foot.
The document also says Smith told a man he had killed nine people and buried them in 55-gallon drums. If the man wasn't careful, he would be next, Smith said, according to the document. Smith denies saying that.
The charges were dropped in 2010 because Smith's behavior "has improved greatly and he has conducted himself in a respectful and civilized manner when interacting with medical staff and other patients," according to the prosecution's petition to dismiss the charges.
Other charges involving veterans don't reach the federal level.
Two weeks ago, a 67-year-old homeless Vietnam veteran was arrested at the downtown VA hospital on a charge of criminal trespass.
Johnny Glasker said he came for an appointment Tuesday, then was told he couldn't linger on the property.
When Glasker returned to talk with his friends, he was told a warrant was out for his arrest.
Glasker said the VA provided him a hotel room for the night and transportation to his appointment in the morning. He wasn't seen until late in the day, however. The hotel room was a one-night deal, so Glasker waited outside for someone to pick him up.
That's when the warrant was activated and Glasker was arrested by Richmond County deputies.
Maj. Gene Johnson, who oversees Richmond County jails, said veteran arrests at the VA are a "pretty common occurrence." Most are on charges of disorderly conduct or criminal trespass, he said.
Robin Brown, the acting public affairs officer for the VA Medical Center, said people who refuse to leave the property can be considered loiterers.
"If their actions reach the point of disrupting the medical center mission of providing medical treatment, our police officers can determine the most appropriate judicial charges for the conduct," Brown said in an e-mail.
Brown said that while the VA is federal property, it has a concurrence jurisdiction, which means both local and federal laws can be exercised.