The 1876 elections was indeed a troublesome period as the election returns from three states were unclear but there was a compromise with Republicans which was called the Compromise of 1877.
This was an informal agreement between the Republicans in Congress, and their Democratic counterparts where the Republicans agreed that if the Democrats lent their support to the Republican president, Rutherford Hayes, the Republicans would not object to pulling federal troops out of the South.
The reason this compromise came about was because there were unclear results from three states and therefore neither Hayes nor the Democratic candidate, Tilden, could claim victory. The Compromise of 1877 fixed this and allowed Hayes to win, but effectively ended Reconstruction.
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