A search warrant was issued by a New Mexico judge for Baldwin's mobile phone last month, but police say that it has not yet been handed over.
Investigators want to scour through messages, photos and call logs relating to Rust, the western which Baldwin was shooting at the time of the tragedy.
In Baldwin's four-minute video, posted on Saturday, he said the allegations that he was not complying with requests for his phone were "b******t".
"Any suggestion that we're not complying, myself and any lawyers I'm working with or whatever, is a lie. It's a lot of work, especially as we go through this process then by all means we will comply," he said.
"This is a process where one state makes the request of another state.
"They're gonna go through the state you live in. And it's a process that takes time."
He added: "They have to specify what exactly they want. You can't just go through your phone and take, you know, your photos or your love letters to your wife or what have you."
Baldwin, an outspoken liberal, also accused Right-wing US tabloids of fuelling the claims for political reasons.
"The best way, the only way we can honour the death of Halyna Hutchins is to find out the truth," he said.
"That's what I'm working toward insisting on demanding that the organisations involved in this investigation."
The actor's broadside comes a month after he broke his silence during an emotional hour-long interview with George Stephanopoulos for US network ABC.
Asked if he felt guilt, Baldwin said: "No. I, honest to God, if I felt that I was responsible, I might have killed myself. And I don't say that lightly. Someone is responsible for what happened, and I can't say who that is, but it's not me.
"Someone put a live bullet in a gun, a bullet that wasn't even supposed to be on the property. There's only one question to be resolved, and that's where did the live round come from?"
He added: "I don't have anything to hide."
