On the spot fine? I'd take a look at the bounty, as Megatrons suggested.
(Being in rl law enforcement, I would suggest that the 'Ways and Means Act' has been used - jerk around the cop, and he'll find something to pin on you).

Just luck that the guard did not notice the sword was stolen.
He could also drag you to the jarl to pay the fine and he would take all you stolen items.
Happened to me in Oblivion, did not notice I was mostly naked until I had left town, I was wearing an stolen guard uniform
