Alec Baldwin

wants a "speedy" trial for the involuntary manslaughter charge he's facing over

Halyna Hutchins' death

.

The 65-year-old actor

was again indicted by a grand jury

in relation to the fatal shooting of the cinematographer on the

set of 'Rust' in October 2021

, and in his first response since the new charge was brought, his legal team have stressed they want things to move quickly in order to "minimise public vilification and suspicion."

According to court documents obtained by 'Entertainment Tonight,' the 'Boss Baby' star's legal team emphasized their "demand for speedy trial, discovery and exculpatory information, notice of defense intent to call witnesses," as outlined by the Sixth Amendment, and also explained they wanted to do so in order to "avoid the dangers of proving his innocence that often arise after a lengthy delay in prosecution."

Alec must enter a plea on 1 February

at 11am, either by phone or video conference.

The former '30 Rock' star had previously had involuntary manslaughter charges against him dropped but last October, special prosecutors announced that they planned to present the case to a Santa Fe grand jury.

They argued that probable cause existed to criminally charge the Hollywood star, explaining that "additional facts" suggested that Alec "has criminal culpability in the death of Halyna Hutchins."

The 'Cooler' actor

has always denied that he pulled the trigger on the prop gun

that killed the cinematographer and offered a potential explanation for what happened on the set during an interview on 'The Chris Cuomo Project' podcast in 2022.

Asked how a gun could be fired without someone pulling the trigger, he replied: "This did not come from me, this came from the DA's Office themselves.

"You're familiar with what fanning a gun is? Have you heard of that phrase, fanning the gun? So, if you pull the hammer back, and you don't lock the hammer; if you pull the hammer back pretty far - in old Western movies you'd see someone fan the hammer of the gun - the hammer didn't lock; you pulled it back to an extent where it would fire the bullet without you pulling the trigger, without you locking the hammer."

In January 2023,

Hannah Gutierrez-Reed - the film's armorer - was charged with two counts

of involuntary manslaughter and tampering with evidence.

She has pleaded not guilty and her trial is set to begin in February.