The Tazy is a breed of sighthound common in Kazakhstan. The identification of runs of homozygosity (ROH) is an informative approach to assessing the history and possible patterns of directional selection pressure. To our knowledge, the present study is the first to provide an overview of the ROH pattern in the Tazy dogs from a genome-wide perspective. The ROH of the Tazy was found to be mainly composed of shorter segments (1–2 Mb), accounting for approximately 67% of the total ROH. The estimated ROH-based inbreeding coefficients (FROH) ranged from 0.028 to 0.058 with a mean of 0.057. Five genomic regions under positive selection were identified on chromosomes 18, 22, and 25. The regions on chromosomes 18 and 22 may be breed specific, while the region on chromosome 22 overlaps with regions of hunting traits in other hunting dog breeds. Among the 12 candidate genes located in these regions, the gene CAB39L may be a candidate that affects running speed and endurance of the Tazy dog. Eight genes could belong to an evolutionarily conserved complex as they were clustered in a large protein network with strong linkages. The results may enable effective interventions when incorporated into conservation planning and selection of the Tazy breed.