There are no Federal regulations in the US that prohibit it. Many states and
municipalities have ordinances that prohibit hand propping without a pilot
at the controls. King County in Washington has such an ordinance, for
example, and the cops have been known to write tickets to pilots hand
propping their planes at Boeing Field.

Having a pilot at the controls is no guarantee of safety. One time I
was demonstrating an old 150 (with a very marginal generator), and
the battery wouldn't crank the engine. I decided to prop it, and had
the prospective buyer sit at the controls. We went through the "Switch
Off and Pull it Through" routine, and at about the third blade - it
started! No harm done, but I sure was startled. He had incorrectly
set the switch to the right mag rather than Off position. In spite
of this and other problems like leaky brakes, he bought the plane!
(it was moving up in the world for him, considering the ratty old
ragwing he arrived in).

David Johnson