The shooting case on the brig "Ottawa" was investigated at New York by Coroner Gover, Monday 1st inst. Freeman TINGLEY the mate, deposed in substance that the vessel sailed from Para, South America on 8th March and on 19th at 7 p.m., he was taking the altitufe of the polar star when Capt. William PYE came up to him and inquired what he was doing, and being answered correctly, he raised a pistol and fired, the shot taking effect in the fleshy part of the thigh. The mate then balloed and ran round the main mast, the captain pursuing and firing another shot which took effect in the left side above the hip. The steward came out of the cabin on the alarm and was also fired at, but not hit. The captain was then secured. No cause is assigned for the deed and it is supposed the captain was laboring under some temporary aberation of the mind, he having attempted to jump overboard after the committing deed. Capt. PYE, who is native of P.E.I., but lives at Hopewell Cape (Albert Co.) N.B. was confined in the tombs to await his trial. He is 28 years of age, the mate, 24.