We present high resolution CO observations of the inner 15 kpc of NGC 1275 (3C84), the giant elliptical galaxy located in the center of the Perseus cluster of galaxies. Both, the intensity distribution of the CO emission and the dynamical properties resemble the interplay of rotation and highly turbulent motion of the molecular gas. The projected rotation velocity of the gas is found to be approximately 100 km/s, however, the line emission is dominated by a high velocity dispersion of sigma(upsilon) > 200 km/s on either side of the nucleus. The origin of the observed features is discussed referring to two scenarios, which have been developed on the bases of optical and X-ray data: First, we may observe the merging of NGC 1275 with an infalling, molecular rich (M(gas) approximately 6.10(9) h75(-2) M.) galaxy. Alternatively, the molecular gas may be a condensation product of the cooling flow of approximately 300 M.y-1 which has been proposed for the center of the Perseus cluster. The dynamical behaviour of the molecular gas, however, supports the view that both processes may be responsible for the features traced by our observations.