We use near-infrared spectroscopic data from the inner few hundred parsecs of a sample of 47 active galaxies to investigate possible correlations between the stellar velocity dispersion (sigma_star), obtained from the fit of the K-band CO stellar absorption bands, and the gas velocity dispersion (sigma) obtained from the fit of the emission-line profiles of [SIII]0.953um, [Fe II]1.257um, [FeII]1.644um and H_2 2.122um. While no correlations with sigma_star were found for H_2 and [SIII], a good correlation was found for the two [Fe II] emission lines, expressed by the linear fit sigma_star = 95.4pm16.1 + (0.25pm0.08)sigma_[Fe II]. Excluding barred objects from the sample a better correlation is found between sigma_star and sigma_[FeII], with a correlation coefficient of R=0.80 and fitted by the following relation: sigma_star = 57.9pm23.5 + (0.42pm0.10)sigma_[FeII]. This correlation can be used to estimate $sigma_star$ in cases it cannot be directly measured and the [FeII] emission lines are present in the spectra, allowing to obtain the mass of the supermassive black hole (SMBH) from the M-sigma_star relation. The scatter from a one-to-one relationship between sigma_star and its value derived from sigma_[FeII] using the equation above for our sample is 0.07dex, which is smaller than that obtained in previous studies which use sigma_[OIII] in the optical as a proxy for sigma_star. The use of sigma_[Fe,II] in the near-IR instead of sigma_[OIII] in the optical is a valuable option for cases in which optical spectra are not available or are obscured, as is the case of many AGN.
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