**Core Concept**
Down's syndrome, also known as Trisomy 21, is a genetic disorder caused by the presence of an extra copy of chromosome 21. Screening for Down's syndrome involves assessing the risk of the fetus having this condition, typically through a combination of maternal serum screening and ultrasound examination.

**Why the Correct Answer is Right**
The American College of Obstetricians and Gynecologists (ACOG) recommends screening for Down's syndrome in the first trimester of pregnancy, ideally between 11 and 14 weeks of gestation. This is because the first trimester screening involves a combination of maternal serum screening for alpha-fetoprotein (AFP), human chorionic gonadotropin (hCG), and pregnancy-associated plasma protein-A (PAPP-A), as well as an ultrasound examination to assess nuchal translucency (NT). The first trimester screening is more sensitive and specific than screening later in pregnancy.

**Why Each Wrong Option is Incorrect**
**Option A:** Screening for Down's syndrome is not typically recommended in the second trimester alone, although it may be offered as a combined test with a detailed ultrasound examination and maternal serum screening between 16 and 20 weeks of gestation.

**Option B:** Screening for Down's syndrome is not recommended in the first month of pregnancy, as the necessary screening tests are not yet available and the risk of miscarriage is higher.

**Option C:** Screening for Down's syndrome is not typically recommended after 20 weeks of gestation, as the risk of miscarriage increases and the accuracy of screening tests decreases.

**Option D:** Screening for Down's syndrome is not limited to women over 35 years of age, as the risk of Down's syndrome increases with maternal age, but screening is recommended for all pregnant women regardless of age.

**Clinical Pearl / High-Yield Fact**
The first trimester screening for Down's syndrome includes a combination of maternal serum screening and ultrasound examination, and is more sensitive and specific than screening later in pregnancy.

**Correct Answer:** C.