It varies from state to state.  In some states, it *is* illegal, *unless*
you have a permit and pass courses on the care of that type of animal.  Some
*cities* outlaw all "dangerous" wild animals (crocs & gators included), no
matter what the state law is, in order to protect their citicens if any of
them were to get loose.  But the autorities don't go around knocking on
every door, checing to see if you have a lion, tiger, or bear (oh my!), so a
lot of people have them even without permits.  Of course, those are the ones
that are kept in poor conditions, and the "owner(s)" know very little on how
to care for them, so when the authorities do find out, they end up getting
confiscated and shipped off to a wild animal refuge (like Shambala in So CA
or the one near Terre Haute IN).

HTH

Sounds like it could be pretty life threatening for a small dog.  When I was
a kid, we had a neighborhood problem with a bobcat.  This was in the suburbs
of Washington, DC.  It was living in Rock Creek Park, a bit outside its
normal habitat.  It killed quite a few dogs and people were afraid it would
attack a child.  They aren't all that big either.

Jo