Background: Early diagnosis of cerebral palsy (CP) in high-risk infants is possible at 3–4 months’ corrected age (CA) using standardised assessments. Aim: To assess the utility of neonatal screening assessments—writhing general movements (GMs) and the Hammersmith Neonatal Neurological Examination (HNNE)—to predict CP/high-risk status at 3–4 months’ CA in extremely preterm infants. Methods: Retrospective cohort study of high-risk preterm infants (born < 29 weeks’ gestation and/or birth weight < 1000 g) attending an Early Neurodevelopment Clinic. Data from neonatal assessments were compared with CP/high-risk diagnosis at 3–4 months’ CA, fidgety GMs, and Hammersmith Infant Neurological Examinations (HINE) using logistic regression, linear regression, and Spearman rank correlation. Results: Two hundred and two preterm infants (median gestation age at birth 27.3 (IQR 25.4–28.3) weeks, mean birth weight 870.3 (SD 248.4) grams) were included. A total of 26 (12.8%) infants received early CP/high-risk diagnoses at 3–4 months’ CA. A lower gestational age (GA) (OR = 0.78; p = 0.029, 95% CI [0.26, 0.97]) and abnormal writhing GMs (OR 1.56; p = 0.019, 95% CI [1.07, 2.27]) were predictive of CP/high-risk diagnosis. Although after adjustment for sex, GA, birth weight, and growth restriction, GA (aOR = 0.67; p = 0.068, 95% CI [0.44, 1.03]) and writhing GMs (aOR = 1.44; p = 0.087, 95% CI [0.95, 2.20]) were not significant, a strong trend still persisted. The HNNE scores significantly correlated with both the HINE evaluation (rs = 0.43, p < 0.001, 95% CI [0.31, 0.56]) and fidgety GMs (rs = −0.10, p = 0.012, 95% CI [−0.32, −0.04]). Linear regression confirmed the HNNE was highly predictive of the HINE (correlation coefficient 0.82; p < 0.001, 95% CI [0.48, 1.15]). Writhing GMs did not significantly correlate with either fidgety GMs (p = 0.723, 95% CI [−0.12, 0.17]) or the HINE (p = 0.173, 95% CI [−0.24, 0.04]). Conclusions: Abnormal writhing GMs in the neonatal period were non-significantly associated with early CP/high-risk diagnoses in extremely preterm infants in a multivariate analysis. Additionally, the HNNE significantly correlated with both fidgety GMs and the HINE.