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The company says only government tests should be considered "objective and accurate."

Tesla's public relations team has decided to question the Insurance Institute for Highway Safety's credibility after the Model S failed to receive a Top Safety Pick award for the second time."While IIHS and dozens of other private industry groups around the world have methods and motivations that suit their own subjective purposes, the most objective and accurate independent testing of vehicle safety is currently done by the U.S. government, which found Model S and Model X to be the two cars with the lowest probability of injury of any cars that it has ever tested, making them the safest cars in history," the company said in a statement to CNBC.

The electric sedan arrived on the market in 2012 as the IIHS introduced its small-overlap test, addressing a common crash scenario that presents unique challenges compared to a moderate-overlap impact and the full-width collision covered by the government's official New Car Assessment Program.

In the small- and moderate-overlap tests, a smaller area of the vehicle structure must absorb the same crash energy that is experienced in the NCAP full-width test. The small-overlap impact is particularly challenging to a vehicle's frontal structure, increasing the likelihood of serious injury via intrusion into the driver space.

In its first IIHS small-overlap test, the Model S driver seatbelt did not effectively restrain the dummy and allowed its head to strike the steering wheel. Tesla revised its seatbelt design in January, however a second round of tests uncovered the same problem and raised new concerns over the vehicle's frontal structure and battery module.

"We would argue, that to be considered the safest vehicle on the road, it should earn a 'Good' rating from the IIHS as well as a five-star safety rating from NHTSA," IIHS research chief David Zuby told CNBC.

The non-profit organization is funded by the insurance industry, aligning interests of public safety and reduced claim payouts.

Many major automakers have introduced mid-cycle updates to address shortcomings in IIHS tests. Tesla's botched attempt to improve the Model S crashworthiness score and then attack IIHS' credibility and relevance could have unintended consequences as a second round of media reports now focus on the company's statement.