Hypernasal speech is a common symptom across several neurological disorders; however it has a variable acoustic signature, making it difficult to quantify acoustically or perceptually. In this paper, we propose the nasal cognate distinctiveness features as an objective proxy for hypernasal speech. Our method is motivated by the observation that incomplete velopharyngeal closure changes the acoustics of the resultant speech such that alveolar stops /t/ and /d/ map to the alveolar nasal /n/ and bilabial stops /b/ and /p/ map to bilabial nasal /m/. We propose a new family of features based on likelihood ratios between the plosives and their respective nasal cognates. These features are based on an acoustic model that is trained only on healthy speech, and evaluated on a set of 75 speakers diagnosed with different dysarthria subtypes and exhibiting varying levels of hypernasality. Our results show that the family of features compares favorably with the clinical perception of speech-language pathologists subjectively evaluating hypernasality.