Yvonne, it all depends on when the person you are interested in was born and when the person got married. The Kingdom of Saxony -- (note that the state is called Saxony in English) -- did not introduce the civil registration of births, deaths and marriages until 1876. A birth record would thus be on file at the Registry Office (in German: Standesamt) in Dresden if the person you are interested in was born 1876 or later, a marriage record if the person was married 1876 or later. If the person you are interested in was born before 1876, there would be no birth record. All that would be available in that case would be the person's church baptismal record. And if the person got married before 1876, all that would be available would be the church marriage record.
I should add here that most German Registry Offices will issue copies of vital records only to direct descendants (children, grandchildren, great-grandchildren, etc.) of the person in question.