  (Abridge) The relationship between coronal line (CL) emission and nuclear
activity in active galactic nuclei (AGNs) is analyzed, for the first time,
based on NIR spectra. The 8 CLs studied, of Si, S, Fe, Al and Ca elements and
corresponding to ionization potentials (IP) in the range 125-450 eV, are
detected in 67% (36 AGNs) of the sample. The four most frequent CLs - [SiVI]
19630\AA, [SVIII] 9913\AA, [SIX] 12520\AA\ and [SiX] 14320\AA, - display a
narrow range in luminosity, with most lines located in the interval logL 39-40
erg/s. We found that the non-detection is largely associated with either a lost
of spatial resolution or increasing object distance. Yet, there are AGNs where
the lack of CLs may be genuine and reflect an AGN ionising continuum lacking
photons below a few keV. The FWHM of the lines profiles increases with
increasing IP up to energies around 300 eV, where a maximum in the FWHM is
reached. For higher IP lines, the FWHM remains nearly constant or decreases
with increasing IP. We ascribe this effect to an increasing density environment
as we approach to the innermost regions of the AGN, where densities above the
critical density of the CLs with IP larger than 300 eV are reached. This sets a
strict range limit for the density in the boundary region between the narrow
and the broad region of 10^8 - 10^9 cm^{-3}. A relationship between the
luminosity of the coronal lines and that of the soft and hard X-ray emission
and the soft X-ray photon index is observed: the coronal emission becomes
stronger with both increasing x-ray emission (soft and hard) and steeper X-ray
photon index. Thus, photoionization appears as the dominant excitation
mechanism. These trends hold when considering Type 1 sources only; they get
weaker or vanish when including Type 2 sources, very likely because the X-ray
emission measured in the later is not the intrinsic ionising continuum.
