Can you attach a child bike trailer to a motorized scooter?

Not like a vespa with a seat, but a small standing scooter that only goes 10 mph

you can,not legal

Sure, but only till the cops see.

you could but it is not legal and it could be dangerous.

even if the cops didn't see that, think of the chances of someone getting serios ingory? on a bike you control every factor of the motion, with a motorized scooter you just tell it wether or not to go, and if it should turn left or right, there is an amazing nomber of things that would all depend on what you were driving on, how the motor worked and so on.