Recent Atacama Large Millimeter/submillimeter Array (ALMA) observations found a positive correlation between the mass of dense molecular gas in the circumnuclear disks (CNDs) and accretion rate to the active galactic nuclei (AGNs). This indicates that star formation activity in the CNDs is essential for triggering the accretion of mass to AGNs. Although the starburst-driven turbulence is a key mechanism for the transfer of angular momentum and the resultant mass accretion from the CND scale to the inner radius, the observational evidence is lacking. We report the very-longbaseline-interferometry (VLBI) detection of the diffuse synchrotron emission on a scale of several tens-pc coinciding spatially with the molecular gas disk recently discovered by ALMA observations in NGC 1275. The synchrotron emissions are most likely resulted from the relativistic electrons produced by the supernova explosions. This is an unambiguous evidence of the star formation activity in a CND. The turbulent velocity and the scale height of the CND predicted from the supernova-driven turbulence model agree with the observations, although the model-predicted accretion rate disagrees with the bolometric luminosity. This might indicate that additional mechanisms to enhance the turbulence is required for the inner disk. We discuss the multiphase nature of the CND by combining the information of the CO emission, synchrotron emission, and free-free absorption.