The determination of the energy source for emission lines in LINERs is one of the most important issues related with active galactic nuclei. Is it a power-law continuum source or a shock? The determination of the energy source is a crucial test whether or not there exist massive black holes in their nuclei. However, we have not reached a conclusion yet, because of the limitations of optical diagnostic line measurements and direct UV spectroscopic searches for power-law continuum. We propose infrared spectroscopy of LINERs which show broad Balmer line components. Although those broad lines are weak, their existence suggests that this class of LINERs might have massive black holes in their nuclei. We will determine the ionization/excitation mechanisms for emission lines for these LINERs, using infrared diagnostic lines, most of which are not observable by ground-based telescopes or are very difficult to measure. Because LINERs with broad Balmer lines are rather common, this is also a critical test of the frequency of massive black holes in galactic nuclei.