Stop Shackling and Detaining Pregnant Women Act This bill prohibits the Department of Homeland Security (DHS) from detaining a woman during pregnancy or postpartum recovery and must immediately release any detainee found to be pregnant, unless such woman presents an immediate and serious threat of hurting herself or others A DHS detention facility may not use a restraint on a detainee who is known to be pregnant, including during labor, transport to a medical facility or birthing center, and delivery, or during postpartum recovery, except for medical or safety purposes. The bill prohibits DHS detention officers from being present during a pelvic exam of a detainee, labor, delivery, or treatment relating to a pregnancy, unless specifically requested by medical personnel. If a detention officer is requested by medical personnel, such officer shall be female, if practicable, and remain at a reasonable distance from the detainee. The bill requires that a pregnant detainee shall have access to health care services, including comprehensive services relating to reproductive health care and pregnancy.