The veteran comedian had previously left an angry message on the phone of show creator Dan Harmon, who accused Chase of being drunk when he made the call.
Harmon later apologised to Chase for releasing the message to the public, while Chase said that leaving the message was "the right thing to do".
A further voicemail message from Chase to Harmon has now been leaked via Celebuzz from March 2011, where Chase complains that the show's edits were ruining the whole programme.
Chase in particular states that a lot of the show's filming has been taken out in favour of developing its plots and characters.
He said: "There are two choices. One is the story line - like everybody gives a s**t about the f**king story when they don't even know who the characters are. Or, there's make people laugh.
"[My scene is] cut down. For what? So people can follow the story line between Joel [McHale] and Gillian [Jacobs]? And love affairs and kissing? Come on, man! You're missing the f**king point!
"I mean, this is not my kind of comedy. I thought you hired me for what I can do that's funny. You've got to give me some range.
"And then you've got some f**king editor with no f**king sense of humour - and no sense of me - cutting things down to the point where I just look like an asshole! I don't like it."
He concludes by saying: "If you want me on this show again, I have news for you - I don't want it. It's just a mediocre f**king sitcom. I want people to laugh, and this isn't funny.
"It ain't funny to me, because I'm 67 years old and I've been doing this a long time, and I've been making a lot of people laugh a lot better than this."
NBC has yet to renew Community for a fourth season, but executive producer Russ Krasnoff recently said he is "pretty confident" that the sitcom will return.
Listen to the new voicemail clip below: