Your hospital might have a list of labs approved by the courts for this purpose. Ask in advance. Getting a list from the family courts seems to me the most likely way that you won't waste your money on a test and then find out later it was not allowed because the lab wasn't certified in your jurisdiction.
If you need the test for child-support purposes, contact the family courts in your area of jurisdiction, and ask the family-law judge's clerk for a list of labs that are certified to do that kind of test. No point wasting your money on a lab if it is not certified.