Fewer and fewer 0% deals are being offered these days because of the solid economy and the Fed raising interest rates. You'll have to check with each manufacturer to see what their requirements are.....they are not static, they will change depending on business climate and other factors.
All I can add to this is what I know based on leasing a Subaru just last week. Subaru Motors Finance (Chase) requires a 720+ score (auto specific, not the general FICO) for a Tier 1 lease rate. My spouse and I came back with a 699 (they used Equifax, which would be common in Minnesota), which was Tier 2. It changed the payment by $15 per month.
I also must agree with what Watchman mentioned mentioned above. I'm seeing more 0.9% and 1.9% advertising as the best offers out there. There are some 0% offers, but they are getting to be fewer.