The letter did include a NHTSA business card.
Business cards can be printed anywhere though. I would probably look up any numbers and email on the business card and make sure it is an official NHTSA contact and then actually try to contact the official NHTSA contact first to verify this is legit (not the cell phone).
How did they even find out about your accident in the first place and mail you a letter (presuming it was mailed)? The envelope probably may tell some info too (if it looks like a legit NHTSA envelope, or something else, although envelopes can be faked too).
A quick google seems to suggest your accident would not qualify for a NHTSA crash technician investigation, given your car didn't need a tow (although perhaps the car you crashed into needed a tow and filed a police report?):
"CISS randomly selects thousands of police crash reports at law enforcement agencies in selected areas across the country. The areas reflect the geography, population, miles driven, and crashes in the United States. To be eligible for the CISS sample, a crash must involve at least one towed passenger vehicle."
Crash Investigation Sampling System | NHTSA
However looking up the name, there is a facebook page that says:
"Crash Technician for NHTSA at KLD Associates"
but second line says "Retired" also, so don't know what to make of that.
Log into Facebook
Twitter account also says "Crash Technician" and has retweets of NHTSA Recalls:
https://twitter.com/rkanavy
Of course anyone can put anything on their own Facebook/Twitter page so it doesn't necessarily mean anything in terms of hard proof.
KLD Associates' website does have it claim to be a contractor for NHTSA to do CISS:
CISS for NHTSA - KLD Associates
USA Spending does say they are legit government contractor:
USAspending.gov
I found this document that does say: "CISS PSU Operations Contractor is KLD Associates Inc."
https://govtribe.com/file/governmen...onse-ciss-injury-tech-cost-dot-pdf#web-viewer
However, I wasn't able to find a personnel list for either NHTSA or KLD Associates.