Last October, after the National Highway Traffic Safety Administration released crash test data for the Model 3, Tesla declared that it had the "lowest probability of injury of any vehicle ever tested by NHTSA."

Two days later, the NHTSA responded in the understated way typical of a federal agency. Without naming Tesla, the NHTSA argued that its "5-star rating is the highest safety rating a vehicle can achieve. NHTSA does not distinguish safety performance beyond that rating, thus there is no 'safest' vehicle among those vehicles achieving 5-star ratings."

But documents recently obtained by the website Plainsite using a freedom-of-information request show that the NHTSA's private communications with Tesla weren't so diplomatic.

"Your company has issued a number of misleading statements" about the NHTSA's findings, the agency wrote in an October 17 letter to Elon Musk. "Your use of NHTSA's 5-star ratings and associated data is inconsistent with" the NHTSA's guidelines."

It wasn't the first time Tesla had quarreled with the NHTSA over this issue. Back in 2013, Tesla made a similar claim about the Model S, declaring that the Model S achieved "a new record for the lowest likelihood of injury to occupants."

The NHTSA appears to reference those 2013 claims in its October letter: "because your company has previously failed to conform to these guidelines, we are referring this matter to the Federal Trade Commission's Bureau of Consumer Protection to investigate whether these statements constitute unfair and deceptive practices."

We contacted the FTC by email, but a spokesman declined to comment, stating that the agency doesn't confirm or deny whether a company is under investigation.

Tesla has stood by its statements, arguing that it's merely relying on statistics calculated by the NHTSA itself.

NHTSA says raw injury scores don’t account for vehicle weight in multi-vehicle crashes

The NHTSA conducts a number of different crash tests for each vehicle and then issues a series of ratings ranging from one to five stars for different aspects of vehicle safety. There's no disputing that the Model 3 performed well on these tests, achieving five stars—the agency's highest rating—across the board.

The NHTSA would have liked Tesla to stop there. Instead, Tesla dug into the NHTSA's data and spotted an opportunity to further toot its own horn. As part of its evaluation process, the NHTSA calculates a number called a vehicle safety score, which the agency has characterized as “relative risk of injury." The agency then awards each vehicle a star rating based on VSS ranges.

Tesla noticed that the Model 3 had a better VSS score than any other vehicle on the market. That, in Tesla's view, means that a Model 3 driver is less likely to be injured in a crash than a driver of any other vehicle.

But the NHTSA argues that this is statistical malpractice because it doesn't take into account vehicle weight. In a vehicle-to-vehicle crash, the occupant of the heavier vehicle is less likely to be injured. The NHTSA's tests, which involve crashing a car into fixed objects, don't necessarily account for this difference.

"A number of NHTSA studies have evaluated the impact of vehicle mass on fatality rates, and these potential safety differences are not reflected in a vehicle's frontal crash test results," the agency wrote in October. "It is impossible to say based on the frontal crash results or overall vehicle scores whether the Model 3 is safer than other 5-star rated vehicles."

Tesla didn't back down in its public statements last October. And its private response to the NHTSA was equally defiant.

"Respectfully, we disagree with the agency's position. Tesla's statement is neither untrue or misleading," a company lawyer wrote on Halloween. "We did not address weight, nor claim Model 3 would outperform substantially heavier vehicles in a frontal head-to-head crash."

Tesla argued that its "blog statements are entirely based on actual test results and NHTSA's own calculations for determining relative risk of injury and probability of injury."

"Based on the foregoing, we do not see a reason to discontinue use of these statements," the company concluded.

Contacted by email, a Tesla spokeswoman declined to comment on the matter further, saying the company stood by the statements it made last October.