The hypothesis of behavioral parameters dependence measured from person's head movements in quasi-stationary state on COVID-19 disease is discussed. Method for determining the dependence of vestibular-emotional reflex parameters on COVID-19, various diseases and pathologies are proposed. Micro-movements of a head for representatives of the control group (with a confirmed absence of COVID-19 disease) and a group of patients with a confirmed diagnosis of COVID-19 were studied using vibraimage technology. Parameters and criteria for the diagnosis of COVID-19 for training artificial intelligence (AI) on the control group and the patient group are proposed. 3-layer (one hidden layer) feedforward neural network (40 + 20 + 1 sigmoid neurons) was developed for AI training. AI was firstly trained on the primary sample of patients and a control group. Study of a random sample of people with trained AI was carried out and the possibility of detecting COVID-19 using the proposed method was proved a week before the onset of clinical symptoms of the disease. Number of COVID-19 diagnostic parameters was increased to 26 and AI was trained on a sample of 536 measurements, 268 patient measurement results and 268 measurement results in the control group. The achieved diagnostic accuracy was more than 99%, 4 errors per 536 measurements (2 false positive and 2 false negative), specificity 99.25% and sensitivity 99.25%. The issues of improving the accuracy and reliability of the proposed method for diagnosing COVID-19 are discussed. Further ways to improve the characteristics and applicability of the proposed method of diagnosis and self-diagnosis of COVID-19 are outlined.