If you deploy any of the three mobile configuration types and they are deployed appropriately, you do not need a mobile XML sitemap file.
In fact, Google's John Mueller said you should NOT have a mobile sitemap for mobile sites. The only case you should have a separate mobile site is when you have a feature-phone (WAP/WML, etc) version of your site, which is something most people don't bother with these days.
But for an ordinary mobile-friendly web site, no new sitemap is needed or wanted. It can actually cause more confusion if you add a mobile sitemap file.
Google's John Mueller said this in a Google Webmaster Help thread:
That SEO tool is wrong, you don't need - and shouldn't have! - a mobile sitemap if your site doesn't have a feature-phone (WAP/WML, etc) version. If your site is responsive and works well on smartphones, that's enough for us (if you use one of the other methods, make sure to follow those instructions separately). Feel free to point them at this thread, if they need more information.
It is rare to see John call something out as 100% "wrong," but here he did.
It is interesting how logic goes out of the window for so many SEOs.
Forum discussion at Google Webmaster Help.