The objective was to determine if a screening tool for obstructive sleep apnea could be used to predict adverse perinatal outcomes. This was a prospective observational study of patients receiving prenatal care and universally screened for obstructive sleep apnea with the STOP Questionnaire (four questions related to Snoring, Tiredness during daytime, Observed apnea, and high blood Pressure). Confounding variables were included in a backwards logistic regression model to predict adverse perinatal outcomes. The study population of 442 women had positive STOP screens (64; 14.5%) associated with preterm delivery and neonatal intensive care unit admissions. For preterm delivery, history of preterm delivery was the strongest predictor with odds ratios of 4.2 (95% confidence interval 2.0–8.8; p < 0.001), followed by STOP, odds ratios 2.8 (95% confidence interval 1.4–5.8; p = 0.004) and nulliparity, odds ratios 2.3 (95% confidence interval 1.2–4.4; p = 0.013). A positive STOP was the only significant predictor for neonatal intensive care unit admissions, odds ratios 2.5 (95% confidence interval 1.1–5.7; p = 0.036). STOP screening test performance indicated low sensitivity but high specificity: preterm delivery (28.3%, 87.4%), neonatal intensive care unit admissions (27.3%, 86.6%), low birth weight (25.0%, 86.9%), and preeclampsia (16.7%, 85.6%). As a stand-alone tool, the STOP Questionnaire has limited performance, but could be explored in combination with other factors that might increase sensitivity to predict preterm delivery and neonatal intensive care unit admission.