We explore a novel use of Large Language Models embeddings to classify autism via parental responses to a questionnaire akin to the Autism Diagnostic Interview-Revised. Our analyses used text embeddings of 12 open-ended responses from 30 parents (18 with autistic children and 12 typically developing) and explored two parental classification approaches: a voting system that utilizes the average predictions of a classifier, treating each question response as an independent sample, and a concatenated approach that classifies parents into autism or control groups based on the concatenation of their text embedding responses. Both methods show promise on detecting which parents have children with autism, with the voting system suggesting better performance as the number of questions increases. Our findings encourage further psychological research to use Large Language Models and the application of text embeddings to automate the administration and analysis of open-ended questionnaires.