In this paper, the spatial optical dark soliton filamentization in a nonlocal self-defocusing Kerr medium is investigated. Theoretically, starting from nonlocal nonlinear theoretical model, we examine the influences of the degree of nonlocality and the attenuation constant on the formation of dark soliton filaments by numerical simulation method. We find that when the input background optical intensity is determined, the greater the degree of nonlocality, the farther the initial point of the formation of dark filaments is and the less the number of dark filaments decreases with the increase of the degree of nonlocality; when the ratio of the background optical intensity to the critical optical intensity is fixed, the degree of nonlocality can hardly influence the number of dark filaments and the number of dark filaments under nonlocality is equal to that under locality. Besides, when the input background optical intensity is determined, the number of dark filaments decreases with the increase of the attenuation constant. Experimentally, by changing the concentration of dye solution and the ellipticity of background light, we discuss the influences of the concentration of sample and the ellipticity of background light on the formation of dark soliton filaments respectively and find that when the input background average optical intensity is determined, the number of dark filaments decreases with the increases of the concentration of sample and the ellipticity of background light; when the ratio of the background average optical intensity to the critical optical intensity is fixed, the concentration of sample can hardly influence the number of dark filaments. Besides, the phenomenon of optical shock wave is found in our experiment.