Arp 220 is the nearest ultra-luminous infrared galaxy. It shows evidence of 100 pc scale molecular outflows that are likely connected with galaxy-scale outflows traced by ionised and neutral gas. The two highly obscured nuclei of Arp 220 are sites of intense star formation, with extreme (far-infrared based) star formation rate surface densities, $ SFR $. Despite extensive investigations that searched for active galactic nucleus (AGN) activity in the Arp 220 nuclei, direct evidence remains elusive. We present JWST/NIRSpec integral field spectroscopy (IFS) observations covering the $0.9-5.1 wavelength range of the innermost ($5 i.e. $1.8 1.5$ kpc) regions of Arp 220. The primary goal is to investigate the potential presence of AGN signatures in the nuclear regions by analysing the spectra extracted from circular apertures with a radius of 55 pc (0.15 around each of the two nuclei. The analysis aims to identify highly ionised gas emission lines (with ionisation potential $> 54$ eV) and other spectral features indicative of AGN activity. Atomic and molecular gas kinematics were also taken into account to study the outflow signatures at $< 60$ pc scales. We identify $ 70$ atomic and $ 50$ molecular emission lines in the nuclear spectra of Arp 220. We used recombination line ratios to measure optical extinctions in the range A$_V 11-14$ mag. High-ionisation lines are not detected, except for the line at 4.49$ which we interpret as due to shocks rather than to AGN ionisation. We identify broadening and multiple kinematic components in the and H$_2$ lines caused by outflows and shocks, with velocities up to $ Significantly higher velocities (up to $ are detected in the off-nuclear regions, but they do not conclusively represent direct evidence for AGN activity. Broad-line region components are not detected in any permitted emission line within the NIRSpec wavelength range. Even with the unprecedented sensitivity of JWST/NIRSpec IFS, achieving an unambiguous identification or exclusion of the presence of an AGN in the Arp 220 system remains challenging because of its extreme dust obscuration.