Q:

Should I refocus if I change the aperture in a DSLR?

The title pretty much says what I want to ask.

A:

Theoretically, camera always autofocuses at the largest possible aperture, and then right before shutter being released, it closes it down. Therefore, no need to do it, since DOF can only increase. 

A:

Focus shift happened with some of the well known vintage manual lenses (read about them on pentax forums). This was always noted in reviews because then you could avoid focusing wide open and then stopping down if it was a known issue. Nowadays with auto focus, you dont get that option. But you can check the focus using the aperture test button. Modern lenses are designed for the "wide open focus, then stop down" mechanism, so the engineers minimize the drift. Howver, it seems sometimes it goes wrong for them:
Even on pro versions
and renowned Zeiss

A:

It really depends... 
With higher F-stop value you will get a deeper depth of field. So, if you foucsed with say F/16, and then you change aperture to a lower value, let's say F/2, the diaphragm opens and your depth of field gets shallower, so you might need to refocus to be sure your subject ist still focused.
However, if you change from a low F-Stop to a higher value, your depth of field gets deeper and you shouldn't need refocusing.
You could check into this as a reference:
http://www.exposureguide.com/focusing-basics.htm

