For the green card, they check you don’t owe taxes or have a crimilar record. I assume a credit check wouldn’t be out of the question because any documentation considered relevant to a particular immigration case can be requested. There is mandatory check for diseases like TB and HIV. Green card applicants must go to a doctor and have HIV test, X-rays and vaccinations if they cannot prove they had them when they were children. Full 10 digit finger prints are also required.
