The 71-year-old Glasgow-born actor and comedian said he did not want to get involved in the debate as he did not want to influence anybody.
The Big Yin, speaking to the BBC from New York, announced he would be in New Zealand when the poll takes place on September 18. He said: "I try to keep away out of it. I don't want to be an influence in it. I don't want to influence anybody.
"A lot of people take your word like it's spun gold as if there's some sense to it, I don't want to influence anybody so I shut up.
"I think the Scots will come to a good conclusion in the referendum. They'll get what they deserve."
Connolly said he felt more of a sense of community among people from a similar background to himself than to Scots in general.
He said: "I've never been a nationalist and I've never been a patriot.
"I've always remembered that I have a lot more in common with a welder from Liverpool than I do with someone with an agricultural background from the Highlands, although I do love them. I love Scotland and all it's different faces. That's why this referendum thing is so difficult. It's a morass that I care not to dip by toe into."
The star was discussing his latest role narrating poems by the 15th-century Scots poet Robert Henryson, which have been translated by the late Irish Nobel Prize winner Seamus Heaney for the animated films Five Fables.
Connolly has previously revealed he had surgery for prostate cancer and was treated for the initial symptoms of Parkinson's Disease last year.
He has since said his health is good and he laughed when discussing his current health. He said: "I'm okay. I'm old and I'm cold. I'm going deaf, I can't walk very well.
"I'm getting a lot better, Someone once said growing old is not for sissies, they knew what they were talking about."