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 requires DHS to use the least restrictive restraint necessary and prohibits certain specified restraint types, including four-point restraints and binding a detainee's hands behind her back. 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.