In this paper, we report the signature of spin gapless semiconductor (SGS) in CoFeMnSi that belongs to the Heusler family. SGS is a new class of magnetic semiconductors which have a band gap for one spin subband and zero band gap for the other, and thus are useful for tunable spin transport based applications. We show various experimental evidences for SGS behavior in CoFeMnSi by carefully carrying out the transport and spin-polarization measurements. SGS behavior is also confirmed by first-principles band-structure calculations. The most stable configuration obtained by the theoretical calculation is verified by experiment. The alloy is found to crystallize in the cubic Heusler structure (LiMgPdSn type) with some amount of disorder and has a saturation magnetization of $3.7\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{B}/\mathrm{f}.\mathrm{u}.$ and Curie temperature of \ensuremath{\sim}620 K. The saturation magnetization is found to follow the Slater-Pauling behavior, one of the prerequisites for SGS. Nearly-temperature-independent carrier concentration and electrical conductivity are observed from 5 to 300 K. An anomalous Hall coefficient of 162 S/cm is obtained at 5 K. Point contact Andreev reflection data have yielded the current spin-polarization value of 0.64, which is found to be robust against the structural disorder. All these properties strongly suggest SGS nature of the alloy, which is quite promising for the spintronic applications such as spin injection as it can bridge the gap between the contrasting behaviors of half-metallic ferromagnets and semiconductors.