Background and Objectives: Autism is a developmental condition currently identified by experts using observation, interview, and questionnaire techniques and primarily assessing social and communication deficits. Motor function and movement imitation are also altered in autism and can be measured more objectively, providing the potential for new quantitative markers to aid in the diagnosis process. This thesis aims to reveal and describe movement pattern differences between autistic and non-autistic individuals and classify the groups by using parametric statistics, machine learning (ML), and deep learning methods. Design, Materials, and Methods: 24 autistic and 22 non-autistic participants performed movement imitation and motor function tasks while their hand and eye movements were recorded. Statistical, ML and deep learning methods were applied to identify kinematic parameters that optimally describe the characteristics and discriminate between groups. As the study was limited by small sample size, due to the costs associated with human participant testing, a substantial amount of methodological work was conducted to find ways to validate ML algorithms both reliably and economically, by not requiring holding out substantial amounts of data for validation. Finally, despite the perception of ML as a ``black box'', methods to explain and interpret ML predictions were also used. Results: The imitation task revealed that autistic individuals imitated movement style less accurately than non-autistic individuals and attention rather than motor coordination was the key determinant of imitation level. The simple motor function task revealed that autistic individuals performed aiming movements slower but more accurately. For the ML work, the main challenges were controlling overfitting and model stability. Fusing eye and hand movement measures from a movement imitation task gave ML classification accuracy of 78%. With motor function data, both, ML with engineered features and deep learning gave over 71% classification performance. For both approaches, the variables which were most important for predictions were consistent with the behavioural differences revealed using parametric statistical tests. Conclusion: There are quantifiable differences in motor function and movement imitation in autism and ML algorithms can achieve statistically significant predictions and shed light on autism-specific motor patterns even when a study has a small sample size.