Correction My Birth Mother Gladys Murphy was Born IN Connecticut IN 1904 According to My Birth Certificate

Since I was born in Oakland, California in 1937, she obviously moved there at some time. I would like to find out anything about her. From the limited research I've been able to do, I think her parents may have been either G. Harry Murphy of 1877 and Clara Murphy of 1865 or Thomas Murphy of 1877 and Catherine Murphy of 1878. Those are the only possibilities I found for parents of Gladys Muprhy, born in 1904 in Connecticut.