Neonatal screening is essential for child health and has the following purposes: (1) pulse oximetry screening to evaluate congenital heart diseases; (2) red reflex examination to investigate eye diseases; (3) newborn hearing screening test to evaluate congenital hearing diseases; (4) tongue test to evaluate the lingual frenulum and identify communication and feeding problems; (5) the Guthrie test to screen for metabolic diseases. This study investigated the prevalence of the five neonatal screening tests and its associated institutional and socio-cultural factors using a cross-sectional study with 415 mother and baby binomials from public maternity hospitals in Natal, RN, Brazil in 2019. Pearson's chi-squared, Mann-Whitney and Poisson regression tests were used, with a significance of p ≤ 0.05 and a 95% confidence interval. The sample loss was 71 mothers (17%). The prevalence in the first week and at the end of 28 days was 93% and 99.5% (pulse oximetry screening), 60% and 97.6% (red reflex examination), 71.9% and 93.6% (Guthrie test), 35.5% and 68.2% (hearing screening test), and 19% and 48.9% (tongue test). Only 152 newborns (36.6%) underwent all five tests. The performance of the tests was associated in the final model (p ≤ 0.05) with the residence of the mothers in the state capital (PR = 1.36; 95% CI = 1.18-1.56) and the provision of guidance for mothers about the five tests in maternity hospitals (PR = 1.30; 95% CI = 1.08-1.67). None of the tests met full coverage, and regional inequities were identified indicating the need to restructure the institutions, training and qualification procedures to improve of the work processes and longitudinal care.