His brother was the notorious John Wilkes Booth who assinated Lincoln.
After John Wilkes Booth's assassination of President Lincoln in April 1865, the infamy associated with the Booth name forced Edwin Booth to abandon the stage for many months. Edwin, who had been feuding with John Wilkes before the assassination, disowned him afterward, refusing to have John's name spoken in his house.
The question asks for a family tie, so above is my answer even though it is mostly post civil war.
Another interesting tidbit on Edwin.
Edwin rescued a man at a train station in Jersey City, hauling him back up onto the platform from which he had fallen into the path of an oncoming train. “Upon turning to thank my rescuer I saw it was Edwin Booth, whose face was of course well known to me,” the rescued man wrote years later, “and I expressed my gratitude to him, and in doing so, called him by name.”
Booth, for his part, did not recognize the man he had saved. Some time later, Col. Adam Badeau, a friend of Booth’s assigned to the staff of Gen. Ulysses S. Grant, wrote Booth to inform him that the man he had rescued was a fellow staff officer: Robert Todd Lincoln, the oldest son of the president.