Empirical studies of cold gas content are essential for comprehending the star formation activities and evolution in galaxies. However, it is not straightforward to understand these processes because they depend on various physical properties of the interstellar medium. Massive Faranoff–Riley I/II type radio galaxies rich in molecular hydrogen with lower star formation activities are known as radio molecular hydrogen emission galaxies (MOHEGs). We present a study of neutral hydrogen-gas-associated radio MOHEGs at redshifts <0.2 probed via the H i 21 cm absorption line. Neutral hydrogen is detected in 70% of these galaxies, which are located at a distance of 8–120 kpc from the neighboring galaxies. These galaxies show a scarcity of H i gas as compared to merging galaxies at similar redshifts. We found no strong correlation between N(H i), N$_{H}$, and the galaxy properties, regardless of whether the H i is assumed to be cold or warm, indicating that the atomic gas probably plays no important role in star formation. The relation between the total hydrogen gas surface density and the star formation surface density deviates from the standard Kennicutt–Schmidt law. Our study highlights the importance of H i studies and offers insights into the role of atomic and molecular hydrogen gas in explaining the properties of these galaxies. In the upcoming H i 21 cm absorption surveys with next-generation radio telescopes such as the Square Kilometre Array and pathfinder instruments, it may be possible to provide better constraints for these correlations.