Johnny Manziel Crash: The Polite 911 Call ... 'I'm Not Hurt'

Talk about cool under pressure ...

Johnny Manziel couldn't have been more polite and composed in the moments after he was T-boned in a hit-and-run incident in Dallas last month ... at least judging by the 911 call.

TMZ Sports obtained the audio from the June 20th incident -- in which Manziel reports that his car door was smashed in by a 4-door Charger that sped off after the collision.

"I'm okay. I'm not hurt ... but I was definitely just in an accident."

Johnny said he also had a witness who will vouch that the QB did nothing wrong.

But the best part of the call is when the dispatcher asks for the caller's name -- and you hear the voice sheepishly respond, "Jonathan Manziel."

As we previously reported, cops are investigating the crash. As for Johnny, he refused medical attention and left for Cabo a few days later.