women have cell-free fetal DNA blood testing, amniocentesis, chorionic villus sampling, or other detailed screenings starting in the mid 30s.

http://www.babycenter.com/0_age-and-fertility-getting-pregnant-in-your-30s_1494695.bc

That age is also when other genetic problems become more of a concern, so experts routinely recommend that women have cell-free fetal DNA blood testing, amniocentesis, chorionic villus sampling, or other detailed screenings starting in the mid 30s.