The Education Department has opened a civil rights investigation into whether Smith College, the women’s school in Northampton, Mass., violated anti-discrimination laws by allowing transgender students to enroll. The inquiry broadens the Trump administration’s bid to limit rights for the nation’s transgender students by targeting school admissions for the first time. Until now, the administration had mostly targeted policies that allowed for transgender women to participate in women’s sports and use women’s bathrooms. By investigating Smith, the administration is raising the question of whether allowing transgender women to enroll at a women’s college — and providing access to “women-only” spaces such as bathrooms, dormitories and locker rooms — violates civil rights protections for women. Kimberly Richey, the assistant secretary for civil rights at the Education Department, said in a statement that “an all-women’s college loses all meaning if it is admitting biological males.” “Allowing biological males into spaces designed for women raises serious concerns about privacy, fairness and compliance under federal law,” Ms. Richey said. “The Trump administration will continue to uphold the law and fight to restore common sense.” A spokeswoman for Smith College did not immediately return a request for comment. About 4.7 percent of college students identify as transgender, according to the Society for Evidence-Based Gender Medicine, a group of doctors and scientists that has called for more government regulation of pediatric gender medicine.