You should refer to the manual for the PSV in question.
But, in general, the manufacturer will publish API orifice areas and API discharge coefficients and ASME (or actual) orifice areas and ASME discharge coefficients.
You can use either set you want, I typically find the ASME area and coefficients give a slightly higher (and in some cases, quite a bit higher for the small orifice PSVs) relief capacity. Though you can also argue that means they aren't as conservative.
DO NOT mix API areas with ASME discharge coefficients or vice versa.