Here are some Google search results. I found it surprising that the first form is the most common (I'd have thought the second):
"What is that to do with" About 323,000,000 results
"What does that have to do with" About 28,000,000 results
"What has that got to do with" About 2,700,000 results
"What has that to do with" About 1,530,000 results