Protecting the Health and Wellness of Babies and Pregnant Women in Custody Act or the Pregnant Women in Custody Act This bill amends the federal criminal code to limit the use of restraints and restrictive housing for prisoners who are pregnant or in postpartum recovery. Additionally, it requires the Bureau of Justice Statistics to include, in the National Prison Statistics Program and Annual Survey of Jails, statistics on the health needs of incarcerated pregnant women. A Bureau of Prisons facility must provide appropriate services and programs to address the health and safety needs of women inmates related to pregnancy and childbirth. The Government Accountability Office must study the services and protections for pregnant incarcerated women in state and local correctional settings.