like mbr said above, the simple answer is no.
one cop i got to know in newport beach (he used to like pulling me over all the time) thought we needed insurance. by the next time i ran into him, we both had researched it and couldn't find anything on the books that said we needed it.
that cop teaches all the other cops the laws on "low speed vehicles," (golf carts, mopeds, us, etc...) and said he'd pasd the word that we don't need it.
for kicks, i found a company that insured whizzers, and they said they could do it. it wasn't cheap, though. i passed.
if you ever get stopped and the cop says you need it, politely tell him it's not required. they usually don't know the laws anyway. if it ends up in court, tell them to show you where iy says we need it.