'Rust' Shooting Search Warrant, Cops Looking into Ammo Supplier

The big mystery in the fatal shooting on the set of Alec Baldwin's movie "Rust" remains ... how live rounds ended up in the weapon, and now investigators are taking a closer look at the film's ammo supplier.

According to a new search warrant, obtained by TMZ, detectives in New Mexico have interviewed a guy named Seth Kenney, one of the suppliers of the ammunition head armorer Hannah Reed used on set.

Cops also spoke to Hannah's father, Thell Reed, who himself is an experienced armorer who has worked with Seth. In the docs, cops say Thell told them he and Seth crossed paths on a different production ... a month or 2 before the "Rust" tragedy.

What's interesting about that is ... Thell claims Seth brought live ammo -- a can with about 200 to 300 rounds -- to that set for the purpose of weapons training. When the training was completed, Thell says Seth took back the remaining bullets, and claims that included some live Colt .45 ammo.

The gun Baldwin fired was a long barrel Colt .45. You see where Thell is going with this -- he told cops the leftover ammo from his production might match that which killed cinematographer Halyna Hutchins.

That's his theory, anyway, and cops are willing to check it out -- the Santa Fe County Sheriff's Dept. got the warrant to search Seth's company, PDQ Arm & Prop.

Presumably, they want to see if the fatal round matches those in the can of live ammo from a couple months ago. The judge signed off, giving detectives the greenlight to scoop up the potential evidence.

And, there's this ... according to the docs, cops also spoke to "Rust" prop master, Sarah Zachry, who said she checked the ammo box -- after Halyna was shot -- and found some bullets that rattled, indicating they're dummy rounds, and others that didn't. That led her to believe there were even more live rounds in the ammo box.

Remember, Hannah's attorneys floated a theory that someone, perhaps a disgruntled crew member, intentionally brought live bullets on set to sabotage the production -- but D.A. Mary Carmack-Altwies has said she isn't buying that.