The aim of the study is to identify objective diagnostic criteria for attention deficit hyperactivity disorder (ADHD) based on the analysis of speech and behavioral indicators. The paper presents the pilot data on the analysis of the speech features and behavioral patterns of 92 children aged 5–13 years with ADHD, ADHD with combined disorders, and control groups. We tested children on their ability to complete the test task “co-op play” of the CEDM method. Different types of data analysis were used - instrumental analysis of speech, expert analysis of children’s behavior, assessment of children’s psychoneurological state by their voice and speech by groups of listeners; automatic analysis of facial expression and ML-based automatic classification of diagnoses of children by their speech. Children with ADHD do not differ significantly from typically developing (TD) children in the analyzed speech features, had lower scores for Play and Behavior scales. Children with ADHD + autism spectrum disorders (ASD) have worse speech characteristics - high values of pitch, lower speech activity, lower scores for behavior and play compared to children in other groups. Our experiments with automatic classification showed that ML model is capable of capturing discriminative features in voice of atypically developing children. Binary classification showed good accuracy when comparing data from children with diagnoses and TD children, and lower accuracy when classifying ADHD + ASD and ASD. The paper discusses the results of the study, notes its limitations and its future research.