A viewer asks if she can put peel-and-stick tiles on a painted concrete floor or whether she has to build a sub-floor.
If the paint is intact, that means that there is no moisture problem pushing up from below and that the paint will work as a primer for the glue. As long as the surface is smooth, go ahead with the vinyl tiles. But remember that any small bumps or cracks in the floor will show through the tiles.
A sub-floor is required if there is a moisture problem, or if the surface is not smooth enough. In addition, a sub-floor provides at least some thermal break by creating an air space between the cold concrete and the final flooring. It can also provide the opportunity to actually put some insulation over the concrete.