Four cases of coseismic changes are observed in water levels recorded at a close network of wells around seismically active Koyna-Warna region in western India during 1997--2000. While coseismic increase of 2--7 cm in water levels is observed for earthquakes of M 4.3--4.7 in three cases, a trough like decrease of 0.4--8 cm is observed at 7 wells for an M 5.2 earthquake. All these earthquakes occurred within the network of wells drilled for the study. Our results suggest that decrease in water levels prior to these earthquakes may be premonitory in nature. We show that magnitude of the earthquake and epicentral distance are two vital parameters to record anomalous changes. In our study local earthquakes of M ≥ 4.3 are recorded at a maximum distance of about 24 km. Our studies provide first observations from a unique experiment in India, which will have implications in developing earthquake prediction models.