Customer needs is ONE aspect of it.
The purist answer is - you should do it on every measurable process you have. Who WOULDN'T want to know how capable they were on everything? More data means better data driven decisions, right?
Unfortunately, they cost to perform. AND some of your tolerances are really easy to hit. So you really want a strategy - let's do them on the things that count.
One of these is what your customer identifies as critical, as everyone has said. But there's a few more sources:
1) YOU may know some items are also critical. Your customer may not be the expert on your product.
2) There may be some features that are very difficult for whatever reason. They may not be critical, but they are still toleranced and just very tricky to make.
3) There may be some features that have little meaning to the part. They may not even be dimensioned or specified. But ... they may give you easy to measure metrics that the process is behaving.
So when you are deciding what to do a capability study, these are good things to think about. By no means do you have to do all of them, there should be some logic surrounding what you pick.