9:58 AM PT -- 6/16 -- Hannah just filed an official response, obtained by TMZ ... in which her attorney claims they've spoken to multiple others on set who all agree Hannah was reliable, competent and most definitely not hungover on the job.

They also state Hannah was not intoxicated the night before the fatal accident, and to claim she was "likely" hungover the day of the shooting is just recklessly false. Hannah's legal team says the allegations are clearly just an attempt to ruin Hannah's character.

9:52 AM PT -- 6/14 -- Hannah's attorney, Jason Bowles, tells TMZ, "The prosecution has so mishandled this case and the case is so weak that they are now resorting to character assassination tactics to further taint the jury pool. This investigation and prosecution has not been about seeking Justice; for them it’s been about finding a convenient scapegoat."

Prosecutors in the fatal "Rust" shooting case are now saying they've got witnesses who will testify the set's armorer, Hannah Gutierrez-Reed, was a bit of a party animal in New Mexico ... and they say she was likely hungover when the live bullet was loaded into the gun.

According to new docs, obtained by TMZ, the Santa Fe District Attorney says they've got witnesses that say Hannah "was drinking heavily and smoking marijuana in the evenings during the shooting of Rust."

They push harder -- saying despite being allegedly hungover, Hannah still put a live round "into a gun that she knew was going to be used at some point by an actor while filming a shooting scene with other actors and crew members."

As we reported, Hannah's attorney Jason Bowles sat down with us in February ... claiming his client tried her best to keep the set as safe as possible, but said she was just stretched too thin on the low-budget flick.

What's more, Jason pointed fingers at Assistant Director Dave Halls -- saying Hannah told him to let her know if Alec Baldwin would be handling the gun in question, but claims she was never given the heads up.

You'll recall, the involuntary manslaughter charges against Alec were dropped in April ... but it's clear prosecutors are still going hard against Hannah.