5-26-64 born DC adopted NC

Hi, I am searching for my birthmother/ birthfamily with no luck. I was born in DC in May of 1964 but adopted by a family in North Carolina. Trying to learn more about being born in one place and adopted in another state. I think my birth parents were most likely from NC. Are there any birth indexes for DC? I am planning a trip to NC for some searching but want to plan what to look for BEFORE I go. Can anyone give me some tips that are not published? Thanks in advance for any guidance!