The seesaw legal battle of Brendan Dassey, whose conviction was questioned in the Netflix documentary series “Making a Murderer,” took another turn on Friday as a federal court in Chicago ruled against him, dealing a major blow to his hopes of being freed from prison.

By a 4-to-3 vote, the United States Court of Appeals for the Seventh Circuit ruled that Mr. Dassey’s confession had not been coerced by police investigators, reversing an earlier decision. Mr. Dassey admitted to assisting his uncle, Steven Avery, in the 2005 sexual assault and killing in Manitowoc, Wis., of Teresa Halbach, a 25-year-old photographer. Mr. Dassey later recanted his confession.

Mr. Dassey and Mr. Avery were sentenced to life in prison after separate trials in 2007. Mr. Dassey was convicted of intentional homicide, sexual assault and mutilation of a corpse.

In the decision on Friday, Judge David Hamilton wrote for the majority: “Dassey spoke with the interrogators freely, after receiving and understanding Miranda warnings, and with his mother’s consent. The interrogation took place in a comfortable setting, without any physical coercion or intimidation, without even raised voices, and over a relatively brief time. Dassey provided many of the most damning details himself in response to open‐ended questions. On a number of occasions he resisted the interrogators’ strong suggestions on particular details. Also, the investigators made no specific promises of leniency.”