The murder trial of a man accused of killing 23 people at a Walmart in El Paso, Texas, in 2019 has devolved into a political circus, with claims that a district attorney’s representative impersonated the son of a victim in order to attack the judge.

According to a report filed in court last week by a lawyer appointed to investigate the matter on the family’s behalf, an attorney personally representing District Attorney Yvonne Rosales was responsible for sending an email in the family’s name criticizing Judge Sam Medrano Jr. and a political opponent of Ms. Rosales.

The district attorney’s office responded to the report on Tuesday, calling it biased and claiming that evidence contained within it, including audio recordings, was improperly submitted.

The allegations in the report are the latest twist in a political feud that has erupted in the aftermath of one of Texas’ most high-profile criminal cases.

The attack on a Walmart in El Paso on August 3, 2019, killed 23 people and injured dozens more. According to authorities, Patrick Crusius, then 21, traveled from North Texas to the border city with the intent of killing Latinos.

Mr. Crusius has been charged with capital murder by the district attorney in El Paso. Mr. Crusius is also facing federal charges in connection with the shooting. The federal case, which is scheduled for trial in early 2024, is expected to be heard before the state case. Federal prosecutors have not indicated whether they will seek the death penalty, as the state has promised. Mr. Crusius has pleaded not guilty to all of the charges leveled against him.

During a hearing on Tuesday, Judge Medrano granted Mr. Crusius’ lawyers’ request for at least 45 days to review the report as the case moves toward an undetermined trial date.

As the state case has progressed, a schism has emerged between Ms. Rosales, a Democrat elected in 2020, and Judge Medrano, a Democrat who was first elected to his position in 2000. Judge Medrano accused Ms. Rosales of “grandstanding” at a July status hearing on the case, saying she hadn’t conferred with the court before issuing a news release claiming the state case could go to trial before the federal case. He placed all parties under a gag order.

Ms. Rosales’ office responded in early September by requesting that Judge Medrano be removed from the case, claiming that he was biased against her. On September 27, a Central Texas judge denied that request. The district attorney’s office filed an emergency petition with the Eighth Court of Appeals this week, claiming that the gag order is unconstitutional and requesting that it be overturned.

An email sent to El Paso journalists in August purportedly from the son of Alexander Gerhard Hoffman, who was killed in the Walmart shooting, has become a focal point of recent activity in the case. The email mentioned complaints against Judge Medrano and slammed a former assistant district attorney who local lawyers say could be a political challenger to Ms. Rosales in 2024.

According to local media reports, the email’s recipients were the same as the district attorney’s press list, and it was written in English and included legal process details. The Hoffmans, who live in Mexico, speak primarily Spanish. The district attorney’s office declined to comment.

Because the gag order appeared to have been broken, Judge Medrano appointed a local lawyer to represent the Hoffman family in the event that they required independent legal representation. On Oct. 6, that attorney filed the informational report on behalf of the family.

According to the report, Ms. Rosales’ personal lawyer, Roger Rodriguez, and his wife, Anne Rodriguez, sent the email while using Mr. Hoffman’s widow’s phone. According to the report, Hoffman family members were unaware of the email’s content.

According to the report, the transcripts are of phone calls between Mr. Rodriguez and members of the Hoffman family, who began secretly recording him because they felt he was threatening them. Those records have been turned over to the Federal Bureau of Investigation, according to the filing.