Hi there - 

No, it's not required by code that you remove the existing roofing felt. It's not even a code requirement that you remove the existing shingles if there's only one existing roof on the house. (It is recommended, though, and your new roof will last longer and perform better if you remove the old roof.)

As far as removing the old felt goes, most of it will probably come off while you're removing the old shingles. It's perfectly fine to leave small pieces of it in place, as long as they are laying flat. If they're folded or bunched up, or if they will prevent the new shingles from laying flat in any other way, you should tear them off.

That's the important thing. You can leave the old felt in place as long as it won't interfere with the new roof laying flat.

Hope this helps!

(I'm assuming you're talking about asphalt shingles.)

- Jack