DENVER—Prosecutors in the Colorado theater shootings acknowledged Thursday that they asked potential witnesses what they said to the defense team, but they denied that was improper.

Prosecutors also denied discouraging witnesses from speaking to the defense or warned them that defense lawyers would manipulate their statements if they did—as defense lawyers alleged last month.

District Attorney George Brauchler responded in a court filing to allegations made last month by the attorneys for James Holmes. Holmes is accused of killing 12 people and injuring 70 in a suburban Denver theater in July 2012.

He pleaded not guilty by reason of insanity to multiple counts of murder and attempted murder. Prosecutors are seeking the death penalty.

Holmes’ lawyers accused prosecutors of improperly interfering with their attempts to interview witnesses and asked Judge Carlos A. Samour Jr. to sanction them. Samour hasn’t said whether he plans to do so.

Defense lawyers alleged that prosecutors and law-enforcement officers have told witnesses that if they spoke to the defense team, their words would be manipulated or their meanings twisted.

The defense also implied that prosecutors had urged witnesses not to speak to the defense and asked witnesses to “surreptitiously report back to law enforcement” on any discussions they have with the defense team.

In his response, the DA said members of the prosecution team or law-enforcement officers have in fact spoken to witnesses who were interviewed by the defense team and asked them if they were willing to recount what they said.

“There is nothing improper about the prosecution’s request” and it isn’t against the law, Brauchler wrote.

Witnesses were told they didn’t have to divulge what they told the defense, he said.

Brauchler denied the prosecution team told witnesses their statements would be manipulated or twisted if they spoke to the defense. But he said the prosecution did tell witnesses if they spoke to the defense—or to the news media, prosecutors, law officers or anyone else—their statements could be used in court or in court filings.

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