Any star you please. Their distances are so great (all > 1 parsec) that it doesn't matter which you use as an observational reference for the sidereal period. Even the stars with the highest proper motion (generally the nearest stars) do not show detectable motion with respect to each other on consecutive nights.
A sideral day is the time taken for one rotation of the Earth relative NOT to the stars, but to the Celestial Sphere, which is considered to be at infinite distance.
Dr. Butler's answer is perfect, and Mr. Wenderoth's is essentially the same. Since all stars (other than the Sun) at so far away that they might as well be infinitely far away for the purposes of determining the sidereal day, no matter what star you use, it takes exactly the same time on any given day for ANY of them to appear to go once around the sky.
However, because of minute changes in the time that it takes the Earth to rotate on its axis, the length of a sidereal day is not constant. Usually it increases by a minute fraction of a millisecond from one "day" to another, primarily due to the gravitational effects of the Sun and Moon, but in recent years the Earth's rotation has been speeding up (presumably due to changes in the motion of material in the molten outer core of the Earth, but that's still a controversial topic).
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