HARTFORD — A court on Monday rejected the appeal of a Connecticut woman convicted in a 1994 murder-for-hire case that landed her in prison for life and was depicted in books and TV shows.Three judges on the Connecticut Appellate Court disagreed with Beth Carpenter’s argument that her trial lawyer made mistakes, including not securing a plea deal and not having an expert witness examine her before the trial.Carpenter intends to appeal the ruling to the Connecticut Supreme Court, said her lawyer, Norman Pattis.“The result is disappointing,” Pattis said. “We remain hopeful that justice will, in the end, be done. Beth Carpenter does not belong behind bars.”Kevin Kane, the state’s top prosecutor, said the court ruling speaks for itself. He said his thoughts are with the victim’s family.Carpenter, now 53, was convicted of murder and conspiracy in 2002 for plotting with her lover and boss, Haiman Clein, to kill her brother-in-law, Anson “Buzz” Clinton. Carpenter and her parents believed Clinton, a onetime exotic dancer, was abusing his 3-year-old stepdaughter, who was Carpenter’s niece. Clinton was shot to death in 1994 in East Lyme.Carpenter, a former lawyer and Ledyard resident, fled to Ireland after the killing and was arrested there in 1997. Before her return to Connecticut, state prosecutors had to agree to not seek the death penalty because Ireland does not allow capital punishment. The state has since abolished the death penalty.Clein, also a lawyer, was the key witness against Carpenter at her trial, testifying that it was her idea to kill Clinton. He said he was in love with Carpenter and believed her niece was being abused, so he paid Mark Despres to kill Clinton.Despres, a drug dealer and one of Clein’s clients, is serving 45 years in prison, and Clein is serving a 35-year sentence.Carpenter said she had nothing to do with the plot and accused Clein of planning the killing without her knowledge because he loved her and wanted to impress her.At least two books have been written about the case, “Murder: A Family Affair” by Ernest Dorling, and “Lethal Guardian” by M. William Phelps. It also has been the subject of several television true-crime shows, including “Snapped” on the Oxygen network and “Mugshots” on truTV.