Galveston was nicknamed the “Free State of Galveston” during the Prohibition because of its illegal liquor, gambling and prostitution. The end of Prohibition and criminal investigations in the 1940s put an end to the era of the ‘Free State of Galveston” by the early 1950s.
 
The nickname “Free State of Galveston” has been cited in print since at least 1938.
 
 
Wikipedia: Free State of Galveston
The Free State of Galveston (sometimes the Republic of Galveston Island) was a whimsical name given to the island city of Galveston in the U.S. state of Texas during the early to mid-20th century. Today, the term is sometimes used to describe the culture and history of that era. This free-wheeling period reached its peak during the Prohibition and Depression eras but continued well past the end of World War II.
 
During the Roaring 20s, Galveston Island emerged as a popular resort town, attracting celebrities from around the nation. Gambling, illegal liquor, and other vice-oriented businesses were a major part of tourism. The Free State moniker embodied a belief held by many locals that Galveston was beyond what they perceived were repressive mores and laws of Texas and the United States. Two major figures of the era were the organized crime bosses Sam and Rosario Maceo, who ran the chief casinos and clubs on the island and were heavily involved in the government and the tourism industry. The success of vice on the island, despite being illegal, was enabled by lax attitudes in the society and the government, both on the island and in the county. In one of the more famous examples of this, a state committee, investigating gambling at the famed Balinese Room, was told by the local sheriff that he had not raided the establishment because it was a “private club” and because he was not a “member”.
 
Much of this period represented a high point in Galveston’s economy. It is sometimes referred to as the “open era” or the “wide-open era” because the business owners and the community made little effort to hide the illegal vice activities. The tourist industry spawned by the illegal businesses helped to offset Galveston’s decline as a commercial and shipping center following a devastating hurricane in 1900. However, crackdowns against gambling and prostitution in Texas during the mid 1900s made these increasingly difficult businesses to sustain. By the 1950s, this era of Galveston’s history had ended.
   
Handbook of Texas Online
GALVESTON, TEXAS. The city of Galveston is on Galveston Island two miles offshore in the Gulf of Mexico, at 29°18’ north latitude and 94°47’ west longitude, in Galveston County.
(...)
During the years between the world wars Galveston, under the influence of Sam and Rosario (Rose) Maceo, exploited the prohibition of liquor and gambling by offering illegal drinks and betting in nightclubs and saloons. This, combined with the extensive prostitution which had existed in the port city since the Civil War, made Galveston the sin city of the Gulf. The citizens tolerated and supported the illegal activities and took pride in being “the free state of Galveston.” In 1957, however, Attorney General Will Wilson with the help of Texas Rangers shut down bars such as the famous Ballinese Room, destroyed gambling equipment, and closed many houses of prostitution.
   
Google Books
Our Ships;
An analysis of the United States merchant marine
By the editors of Fortune
New York, NY: Oxford University Press
1938
Pg. 236:
It is a sailor’s paradise whose chief means of livelihood are tourists and transportation and whose freedom in matters of entertainment has earned it the title of the “free state of Galveston.”
   
21 November 1944, Cleveland (OH) Plain Dealer, “Pigs in Old Texas Effect on Politics breath of Liberty” by Richard T. F. Harding, pg. 22, col. 1:
Freedom at a Focal Point
Even more than size, independence is the word for Texas. The idea, running with unusual strength through the state’s history, seems to appear with unusual force in some communities. “Gentlemen,” said one of the hosts on a launch going up the Houston ship channel, “you are just leaving the Free State of Galveston.”
   
Google Books
Proceedings [of the] regular meeting, Volume 37
Northwest Shippers’ Advisory Board
1948
Pg. 45:
Gentlemen, it is a privilege to welcome you to the “Free State of Galveston.” We are always happy to have visitors down here. Especially are we flighted to have people come in who talk and understand our language — that is shipping.
   
2 October 1949, Galveston (TX) Daily News, pg. 1, col. 4:
“FREE STATE”
OF GALVESTON
BRINGS QUERY
The city of Galveston has many reasons to justify its fame across the land, but E. S. Holliday, general manager of the Chamber of commerce, believes he has found another one.
 
In his mail, the other day, Holliday received a letter from the little city of Hope, Ark. (pop. 7500), in which his correspondent, Charles V. Fox, asked for explanation of the term: “Free State of Galveston.”
 
Wrote Fox:
 
“A friend of mine insists that the city of Galveston is not in or a part of Texas, nor the United States, because it is separated from both by water. He claims the citizens do not take part in Texas nor United States elections, nor is the city nor its people obligated to pay taxes to either.
 
“Is he right or wrong? I can’t see any logic in his opinion, but I would like for you to give us the facts. I thank you for this favor.”
 
With a wishful sigh, Holliday replied that Galveston (alas!) must pay taxes both to the state and national governments and that its residents are considerably harassed therein.
 
However, Holliday added, the city is truly known as the “Free State of Galveston” because it is the place where people from over the Southwest congregate for their vacations and conventions and these visitors are always “free” to enjoy themselves as they wish.
 
Further to bolster his information that Galveston is a part of the United States, Holliday cited statistics which rate Galveston as the third largest port in the nation—and Texas and the nation could hardly get along without it!
 
Google Books
U.S.A. Confidential
By Jack Lait and Lee Mortimer
New York, NY: Crown Publishers
1952
Pg. 213:
The inhabitants, 80000 they claim, like to talk of it as the Free State of Galveston. They do not regard it as part of Texas, which willingly disowns it as the bad boy of a good family.
 
22 May 1955, Dallas (TX) Morning News, pt. 1, pg. 11:
A REPORT ON GALVESTON
There’s Gambling, Drinking
But the Crime Rate’s Low
(Editor’s Note: The Associated Press sent Max B. Skelton to Galveston for a story on the resort city after the newly elected mayor announced he favored regulated gambling and prostitution. For four days, Skelton visited all sorts of establishments and talked to persons in all walks of life.)
By MAX B. SKELTON
GALVESTON, Texas (AP).—An individual’s likes and dislikes are respected on this island of contrasts, the Free State of Galveston.
 
Stories about Galveston having swank gambling clubs and liquor-by-the-drink “social clubs” are true—but you have to look for them.