Attention-deficit hyperactivity disorder (ADHD) affects at least 5% of the world population and can disturb normal development causing serious issues in adulthood. Therefore, it is important to develop tools to help detecting ADHD so that treatment can start as soon as possible. Plus, the differentiation of ADHD in its subtypes is important to define the recommended treatment. Here we present original research to investigate the hypothesis of using a Spiking Neural Networks (SNN) EEG signals classifier for automated diagnostic of ADHD subtypes. This research used data from 243 patients and healthy volunteers acquired as part of the Healthy Brain Network. These resting state EEG signals were collected from 5-minutes scan with a 128 channel 500 Hz system. For benchmarking, we present a comparison of the SNN performance with a support vector machine, a k-nearest neighborhood, a random forest algorithm and a multi-layer perceptron. We present experiments for both the diagnostics of ADHD and for detecting which ADHD subtype the patient has. SNN presented a 72.00% accuracy for detecting ADHD surpassing all the other techniques by 9.1 % and 68% in detecting if the subject is a member of the Combined ADHD, Inattentive ADHD or control groups (18% better than the second-best technique). Clinical Relevance - This work has shown a resource that can be useful allied to other tools to help diagnosing ADHD and its subtypes.