Modern DSLR cameras come with rolling shutter. My Nikon has visible rolling shutter (in certain conditions).
I don't know whether exceptions exist.
Yes, this site says that CMOS have a rolling shutter and CCD uses total shutter.
Here is a search showing all cameras with a CCD sensor. Here is the same search but showing DSLR cameras only. There are no results for the second search.
However, you should consider whether rolling shutter is a problem for you. For me it is not. You can work around it in most situations, you can also remove some of it in post (premiere pro, apparently). But if you are concerned about this for video shooting, you should ask on http://avp.stackexchange.com.