Aiming to support projects and managements of irrigation for vegetables in the Mid-North region of Mato Grosso state, Brazil, this paper determined crop evapotranspiration (ETc), crop coefficients (Kc) and water response function of summer squash (Curcubita pepo) cv. ‘Italiana’ under different cultivation conditions. The plantations were conducted in the dry season of the region (July to October 2016), using 2.5 kg m-2 of millet straw (grass) and crotalaria straw (legume) and bare soil. ETc was obtained by soil water balance through tensiometry, whereas Kc values were given by the ratio between ETc and the reference evapotranspiration (ETo) obtained by the FAO-56 Penman-Monteith method. For the water response function, the rates of 40, 60, 80, 100 and 120% ETc were applied, in which case the Class A pan method was used to obtain ETo. The different soil covers did not influence the ETc, Kc and accumulated thermal sum in the phenological stages of the summer squash. Kc values were 0.1, 0.25, 0.38 and 0.41, for the phenological stages I to IV, with average durations of 8, 46, 16, and 20 days, respectively. Increase in irrigation depths did not influence the rates of production of male and female flowers, but affected yield and decreased water use efficiency, regardless of soil cover.