Louisiana has dismissed all charges against a man who spent several years on death row after his infant son died in 2012, in a case that drew national attention to a parish that sentenced young black men to death at an unusually high rate.

Rodricus Crawford, 28, a resident of Caddo Parish, La., in the northwestern corner of the state, was sentenced to death in 2013 after prosecutors argued that he had suffocated his son. But Louisiana’s supreme court threw out his conviction in November after finding that the jury selection in his case may have been racially biased. Mr. Crawford was released from prison later that month.

In a statement announcing that it would not retry Mr. Crawford, the Caddo Parish District Attorney’s Office acknowledged evidence suggesting that at the time of death, his son had pneumonia and bacteria in his blood that indicated sepsis. The state said that it could not meet the burden of proof to gain a new conviction for Mr. Crawford.

Cecilia Kappel, one of Mr. Crawford’s lawyers, described him in an interview on Thursday as someone who should never have been facing such a stark sentence to begin with.