BOSTON — In the final episode of his closely watched criminal case, Survivor star Richard Hatch failed to persuade appeals judges here to free him from federal prison or reduce his sentence.

In a decision released yesterday, the U.S. District Court of Appeals upheld his conviction for tax evasion and his 51-month sentence.

In 2006, a jury in U.S. District Court, Providence, found Hatch guilty of not paying the taxes he owed on about $1.4 million, including the $1 million prize he collected for winning the first season of the reality show. He was convicted of filing false tax returns and given the maximum sentence allowed after Judge Ernest C. Torres concluded that he had obstructed justice when he “willfully gave false testimony.”

Hatch, 46, of Newport, is serving his sentence in a federal prison in Morgantown, W.Va. He won the first season of the seminal CBS show and became infamous as the cunning and openly gay contestant who competed in the nude.

In the appeal filed on Hatch’s behalf, his Texas lawyer, Michael Minns, argued that Torres prevented him from adequately exploring a key part of his client’s defense — that Hatch thought CBS would pay the taxes on his winnings. Hatch maintains that the show’s producers, Survivor Entertainment Group, allowed food to be smuggled to a rival contestant and that when he confronted producer Mark Burnett about it, he was led to believe that if he won the show’s jackpot he would be off the hook for the taxes.

But the appeals judges agreed with prosecutors, who maintained that Torres simply sought to curtail broad questioning about cheating on the show while still inviting Hatch’s lawyer to explore any tax deals and what led to them.

“The court understandably observed that the details of how the show was being staged were not in themselves relevant to Hatch’s state of mind when he filed his tax returns almost two years later,” the decision reads. They quoted Torres as saying, “You can certainly get into anything that Mr. Hatch has to say on the rules of how he was going to be compensated if he won.”

The appeals judges noted that Burnett was called as the government’s first witness and that Hatch’s legal team “never asked him on cross-examination whether he or others at SEG had promised that SEG would pay Hatch’s taxes — nor did the defense later call Burnett as its own witness and seek to elicit such testimony.”

Furthermore, Hatch himself “never testified at trial to the events and words by Burnett or others that might constitute a quid pro quo deal … although specifically invited to do so by the court on several occasions.”

Regarding Torres’ decision to give Hatch the maximum sentence, the appeals judges concluded that Torres “catalogued many instances in which Hatch had committed perjury.”

rsalit@projo.com