I can only give general information here, as to really answer your questions requires a very local expert.
Bar leagues, in general, are not affected by a state's gambling law because, if they are truly FREE (I note you put that word in quotation marks) they are not gambling under any state statute. "Gambling" always requires 3 things: Prize, chance (to one degree or another) and consideration. "Consideration" means a payment, or an obligation to pay, something of value for the chance to win the prize. If entry into the poker game is truly free, no hidden costs, it is not gambling.
Now we get into the details. In the few worst states, merely making money by the selling of extra drinks has been said to meet the consideration requirement (like when a bar makes you buy a "drink card" to enter the game), in other states there must be some direct fee paid by the player, like a "dealer fee." In most states, so long as there is truly no fee or money taken from the players, the fact that the free game produces extra patrons for the bar (who is usually the one paying the league operator to run the game) does not mean a bar league game violates the gambling laws. But aside from that, each state has its own agency regulating bars and the rules of that agency may allow or not allow such games regardless of whether they are free or not. Local towns and sometimes counties also sometimes have laws governing when such games might be allowed and when they are not. THE ONLY PERSON WHO CAN REALLY GIVE YOU A DEFINITIVE ANSWER IS A LAWYER FAMILIAR WITH YOUR STATE'S AND LOCALITY'S LIQUOR LAWS AND REGULATIONS. It takes some research, but is not the kind of task that would take a competent business attorney a long time to figure out.
If you cant get your lawyer to find this out, the PPA might be able to give you the names of lawyers in your area more familiar with the subject. Send us an e-mail for that referral if you need it.
For some basic information about the legality of bar leagues in your locale, I would suggest contacting whatever agency is in charge of licensing the bars in your area (usually called the "state liquor commission," but not always).
I am not aware of any "hotlines" on this subject, but "bar leagues" are quite popular around the country and I am sure you can find other leagues to contact by searching the internet.
Sorry this was not completely helpful, but while gambling laws have similar general patterns, what is allowed or not allowed to happen in bars is truly a state by state and local by local answer depending primarily on the liquor laws.
Skallagrim