DAT-HET rats with their underlying hyperdopaminergia are a promising model for the investigation of neuropsychiatric diseases, which are based on impaired dopamine neurotransmission, including alcoholism. The aim of the work was to evaluate the effect of free alcoholization on drinking, locomotor, exploratory behavior, anxiety, and Tyrosine hydroxylase (TH) levels in rats with impaired functioning of the DA system (DAT-HET). The study was carried out on adult male rats of the DAT-HET (n = 15) and Wistar (n = 13), which were divided into 4 groups: “DAT-HET ethanol” (n = 10) and “Wistar ethanol” (n = 9), who were in the mode of free alcoholization for 112 days of the experiment. The DAT-HET water (n = 5) and Wistar water (n = 4) groups did not have access to an ethanol solution and did not participate in behavioral tests. Ethanol preference and consumption was assessed in the “Two-bottle test”. The amount of ethanol consumed in the cells was recorded weekly. Behavior was assessed using the Open Field and Elevated Plus Maze tests. After alcoholization, to assess the level of TH, an immunohistochemical (IHC). It was found that during free alcoholization, DAT-HET rats do not form preferences for ethanol. Under the low ethanol consumption, the initial hyperactivity in DAT-HET rats is leveled. The DAT-HET model leads to an increase in TH levels in NAcc. In addition, the free alcoholization reduces the level of TG in NAcc with the development of a pathological increase in TH, observed in the DAT-HET model, but has no effect on healthy animals.