what state has no poisonous snakes

Neither Alaska nor Hawaii have any native venomous snakes- actually, neither has ANY native land-dwelling snakes (Hawaii has some sea snakes around- but they are pretty rare, and some of them are venomous.)

Hawaii, however, is a prime spot for snakes, so some species have settled there after being imported one way or another. A small worm-like blind snake, the Brown Tree snake, and boas show up in numbers enough to suggest active breeding.

Brown tree snakes are mildly venomous, but not enough to be a threat to humans. The bigger threat is that they eat birds- lots of birds, and have eliminated huge numbers on the islands they have been introduced to.

Being a tropical paradise, any snake some bozo lets go there will probably live quite nicely, so every so often they find something like a viper running around- but you find that in most cities every blue moon.

Maine is ALMOST venomous snake-free. The Timber rattler can be found, sometimes, in the southern tip of the state. These may be transitorty or relic populations, and almost don't count.

Many states have such low numbers of venomous snakes that bites are almost unheard of- in fact, many states don't even bother stocking anti-venin anywhere since they just never need it and it is too valuable to let go bad.

If you are asking this for trivia, I'd go with Hawaii, Alaska, and Maine.

if you need ONE state free from ANY venomous snakes, I'd go with Alaska.