Tulsa, Oklahoma (CNN) Amid growing scrutiny over whether a 73-year-old volunteer deputy who killed a suspect during a sting operation was qualified to be policing the streets, a new report raises a troubling allegation.

Some supervisors at the Tulsa County Sheriff's Office were told to forge Reserve Deputy Robert Bates' training records, and three who refused were reassigned to less desirable duties, the Tulsa World newspaper reported.

Claims that the volunteer deputy's records had been falsified emerged "almost immediately" from multiple sources after Bates killed Eric Harris on April 2 , reporter Dylan Goforth said. Bates claims he meant to use his Taser but accidentally fired his handgun at Harris instead.

The newspaper's story does not say who allegedly asked the supervisors to falsify the training records or why. But the orders apparently started years ago, before Harris' death, "back when (Bates) was trying to get on as a deputy," reporter Ziva Branstetter told CNN's "New Day."

The Sheriff's Office denied the allegations in the Tulsa World's report. It also declined a CNN interview to respond to the claims.

In an email to CNN, the department's Maj. Shannon Clark said the lack of named sources in the newspaper's report leaves him dubious.

"Just keep in mind that the Tulsa World reporter cannot validate her sources and claims anonymity, which leaves us skeptical that her claims are unsubstantiated and deceptive," Clark wrote.

Clark Brewster, an attorney who represents Bates, said the accusations are based on an affidavit from a former Sheriff's Office employee who's now facing a first-degree murder charge.

"I don't put a lot of stock in that report or the credibility of who would further that report," Brewster said.

In a later interview with CNN affiliate KOKI , Clark cast further doubt on the document, which has the name of the accuser blacked out.

"If you're telling us we did something, then why can't you tell us who the person is on that affidavit so we can go back and confirm that information?" Clark said.

Department declines request for details

Sheriff Stanley Glanz and other sheriff's officials have repeatedly insisted Bates was properly trained.

The Tulsa County Sheriff's Office has released a summary of Bates' training courses only over the past seven years.

The office rejected CNN's request for the full training records because Bates' case is under investigation.

Branstetter said she's run into similar obstacles when asking for the names of supervisors who'd signed off on Bates' training records.

"You would think the Sheriff's Office, if in fact there has been no pressure applied, no falsification of records, that they would be forthcoming with these documents," she told CNN's "New Day."

"We've asked for them. They've said they don't believe they're public records."

JUST WATCHED Report: Bates donated cops cars to sheriff's office Replay More Videos ... MUST WATCH Report: Bates donated cops cars to sheriff's office 01:06

Missing gun certification records

Bates was classified as an advanced reserve deputy for the Sheriff's Office. That means he would have had to complete 480 hours of the field training officer program to maintain that classification, the paper said.

Bates would also have needed firearms certification training.

But the sheriff himself has acknowledged there is a problem with Bates' gun certification records -- his office can't find them.

"Bob went out and qualified with three different weapons with an instructor," Glanz told KFAQ radio this week.

He said Bates "qualified with a young lady that was a firearms instructor." But she is no longer there.

"She has left the Sheriff's Office and is now a Secret Service agent," Glanz told KFAQ. "And we're trying to get a hold of her and talk to her about ... we can't find the records that she supposedly turned in. So we're going to talk to her and find out if for sure he did qualify with those."

Inconsistent statements

Even before the Tulsa World story, inconsistencies were apparent in Bates' history with the Sheriff's Office.

In his statement to investigators, Bates said he "became an advanced TCSO Reserve Deputy in 2007."

But the Tulsa County Sheriff's Office has said Bates had been a reserve deputy since 2008

It also said Bates had undergone 300 hours of training. That would be less than the 480 hours of field training that the Tulsa World said is required to be an "advanced" reserve deputy, which Bates claimed to be.

In a statement he made to investigators after the shooting, Bates said the gun he used was his personal weapon, adding that he last qualified at the range in autumn.

He also said he'd attended "numerous schools and seminars related to drug investigations and the tactical operations associated with the apprehension of suspects involved in drug trafficking," a five-day homicide investigation school in Dallas and training from Arizona's Maricopa County Sheriff's Office on responding to active shooters.

But an Arizona official told CNN Bates never trained with the agency.

"He didn't come to Arizona," the official from the Maricopa County Sheriff's Office said, "and he certainly didn't train with us."

Brewster said that line in Bates' statement was referring to a lecture given at a seminar in Washington by Maricopa County Sheriff Joe Arpaio. The seminar was part of extensive training Bates received at classes across the country and through work in the field, he said.

"He met every training regimen," Brewster said. "He met every requirement, and all he did was give of himself."

Who's investigating?

Bates is now charged with second-degree manslaughter for Harris' death. He turned himself in to authorities Tuesday and immediately posted bail of $25,000. His attorney has said he's not guilty, calling the death an "excusable homicide."

The lawyer for Harris' family claims Bates wasn't qualified to be on the force, but received preferential treatment because he'd made donations to the agency and was a friend of the sheriff -- an accusation officials deny, saying they stand by his training record.

Tulsa Police Sgt. Jim Clark, who has been brought in to review the case, has said Bates fell "victim" to something called "slip and capture," a term to describe a high-stress situation in which a person intends to do one thing and instead does something else.

It's a controversial claim that hasn't convinced critics of the department, and calls for an independent investigation into the Sheriff's Office and the case are growing. Earlier this week, the office spokesman rejected any idea of outside investigators into the shooting.

"We're not scared to prosecute our own. ... There's nobody in this culture that can be tougher on cops than their own," Clark said. "You know that analogy that you'll eat your young? You know, that's the same thing in law enforcement. If we have a dirty cop in our ranks, we will disclose them much quicker than the media."

A spokesman for Oklahoma Attorney General Scott Pruitt said his office is concerned about allegations reported in the media about the case "and will continue to monitor and assess what appropriate measures, if any, are warranted."

Glanz has stated publicly that he's reached out to the regional office of the FBI to look into the shooting.

Special Agent Terry B. Weber told CNN there's no open FBI investigation into the case.