MIAMI -- Like many Cuban baseball stars, outfielder Leonys Martin dreamed of leaving the communist island for the bright lights and big money of Major League Baseball.

Martin accomplished his goal in 2011 when he signed with the Texas Rangers, but not before what court documents and the U.S. Justice Department describe as a harrowing ordeal in which he was held for ransom in Mexico while his family members were kept under surveillance in South Florida.

Three people have been indicted in Miami on federal charges of hostage-taking and extortion conspiracy -- counts that carry potential life prison sentences if they are convicted -- and Martin himself is suing his alleged kidnappers for the return of more than $1.3 million he has already paid them.

Andrew Zimbalist, a Smith College professor who specializes in sports economics, said the Martin case appears unique.

"I have never heard of a kidnapping case like this," Zimbalist said.

Many Cubans have defected over the years to play baseball in the U.S., including such current stars as Cincinnati Reds pitcher Aroldis Chapman, Los Angeles Dodgers outfielder Yasiel Puig and Oakland Athletics outfielder Yoenis Cespedes. In September, the Cuban government reversed decades of policy by announcing that its athletes will be allowed to sign contracts to compete in foreign leagues without defecting.

Compared to the vast majority of immigrants, Cubans get unique treatment by the U.S. government under the "wet foot, dry foot" policy that came about during the Cold War. Cubans who reach U.S. soil are generally allowed to stay in this country, while those intercepted outside the U.S. are sent back home.

Martin, 25, a speedy center fielder for the Rangers, made his MLB debut in September 2011. Last season, in 147 games, he hit .260 with 49 runs batted in and 36 stolen bases. Martin and his attorney, Paul Minoff, declined comment for this story, as did the Rangers and MLB officials, citing the ongoing litigation.

A few years before joining Texas, Martin was a rising star in Cuba, traveling to baseball tournaments around the globe with the national team. After an August 2010 tournament in Japan, according to his lawsuit, he decided to leave for the U.S.

He and family members and friends made contact with a man who offered them a trip from Cuba on a yacht to Cancun, Mexico. From there, they could eventually cross by land into the U.S. But instead of journeying directly north, they were taken to a house lined inside with mattresses and watched by two armed men, one of them identified as Eliezer Lazo.

"You are worth a lot," Lazo told Martin, according to the lawsuit. "I am not going to let you go."

Lazo is one of the three people charged criminally in the Miami federal indictment. He is serving more than five years in federal prison in Mississippi for money laundering and other crimes related to a South Florida health care fraud scam. Lazo has not yet entered a plea in the Martin case and court records do not show a lawyer for him.

Eventually, Martin and other unidentified Cuban players were taken to a compound called "The Ranch" near Monterrey, Mexico, where they were supposed to train. Martin's family and friends were taken across the U.S. border at Laredo, Texas, and put on a bus to Miami where they would live for five months in a townhouse owned by Lazo, according to the lawsuit.

In Mexico, there was a nearby baseball field where the players would train and play games before U.S. scouts, and Martin was introduced to another man he was told would be his agent. He was also told he had to sign a contract with an entity linked to Lazo called Estrellas del Beisbol (Baseball Stars) in which he promised to pay 30 percent of any future salary or bonuses -- well above the 5 percent players typically pay.

"Martin had no choice but to sign it (as did the other players with him) considering that they were all being held hostage," Martin's lawsuit says.

Even though Martin did eventually pay Estrellas del Beisbol $1.35 million, the Mexican-based entity claimed in a 2012 lawsuit that Martin wasn't living up to this contract. In his lawsuit, Martin claims it should be declared void because he signed it "under extreme fear and duress" and seeks return of his money.

Estrellas del Beisbol describes itself in court documents as "a baseball academy that cultivates and trains amateur baseball players who desire to play professional baseball in the United States."

In reality, according to Martin's lawsuit, the company is a front for human smuggling and trafficking.

Two U.S.-based attorneys for Estrellas del Beisbol did not respond to emails this week seeking comment on Martin's allegations.

The federal indictment seeks forfeiture of the interests of Lazo and others in Estrellas del Beisbol as well as a bank account belonging to the company. Prosecutors also want money the company may have obtained through other baseball player contracts.