I think those details will come out at the trial too.
One would think that if he is a trooper in uniform, in a marked cruiser, he would also have a small notepad in his shirt pocket to go with his pen. Most cops carry one, and that's the first thing they pull out when asking someones name on the street.
On the other hand, the circumstances may have not allowed the time to do that if he was trying to catch up to him, or trying to read the plate from a distance etc.
Hard to say.
What doesn't sound very plausible to me, is this Trooper would drive to AO's house to question him, leave his card, and then return the next day. I would think a Detective would have done that part.