First, just for fun, I want to mention my closest relative who won an Emmy, back in 1974 (The Snoop Sisters), my second cousin, twice removed, Mildred Natwick. https://www.wikitree.com/wiki/Natwick-16
This was a fun group to look at! It looks like a lot of us have some distant cousins in this group, from the responses so far.
Dolly Parton is my closest connection, at 19 degrees. She is also a distant cousin--14th cousins, once removed.
Some more distant cousins in this group:
John Lithgow--11th cousin
Lin-Manuel Miranda--17th cousins, once removed
Gillian Anderson--18th cousins, twice removed
Michael Douglas--19th cousins, twice removed
From MyConnections, I also found out that Kyra Sedgwick is my 9th cousin, once removed, and Cloris Leachman is my 10th cousin.