I don’t think there are ever any requirements to give birth (after all, you could in theory do the whole thing without ever seeing a doctor or any representative of the state), although there are highly recommended tests. Mostly these are tests for the mother to determine her health status and check for certain conditions such as anemia, thyroid disease, gestational diabetes, pre-eclampsia and certain infections. These tests are done on blood, urine, and vaginal swabs, and blood pressure is also monitored. If both parents are from certain ethnic groups then tests for genetic disorders are usually recommended – for example, Tay-Sachs and other similar conditions for Ashkenazi Jews and sickle-cell trait for people of African descent. In general a person can refuse any medical care, so in that sense they’re not “required” (and certainly plenty of women get no prenatal care at all), but I suppose if parents were refusing to have these tests done for no good reason, a doctor might start to be concerned about negligence.