Children with Cleft Lip and Palate (CLP) may experience difficulties in oral communication, leading to other developmental problems such as delayed language acquisition and poor social skills; thus, early treatment is essential for successful speech rehabilitation. In this paper, we propose a methodology for automatically assessing the phonological precision of children with CLP. We propose to use the probabilities obtained from a phonological class recognizer to measure phonological precision during connected speech. Furthermore, we compute the nasal-to-sound ratio to improve the automatic detection of the nasality level. For this, we considered speech recordings of 88 children with CLP, assessed by a clinician according to four nasality levels: normal, mild, moderate, and severe. We obtained an F1-score of up to 0.54 for detecting the nasality level automatically. The results suggest that phonological analysis can be used for individualized speech rehabilitation.