In this paper, we report the local structure studies in CoFeMnX (X = Si and Ge) Heusler alloys using extended X-ray absorption fine structure (EXAFS) measurements. CoFeMnGe (CFMG) is found to exist in a well-ordered LiMgPdSn structure, while a large amount of antisite disorder is observed for CoFeMnSi (CFMS). CFMG is half-metallic ferromagnetic in nature, while CFMS is a spin gapless semiconductor (SGS). The presence of well-ordered crystal structure is an essential requirement to obtain high spin polarization in half-metallic materials, while SGS materials are supposed to be robust against chemical disorder. The fact that CFMS shows a high spin polarization of 64% even when having a high degree of disorder confirms that the SGS materials are robust against structural disorder.