Plaster of Paris is chemically known as calcium sulfate hemihydrate. Its formula is:
\[
\text{CaSO}_4 \cdot \frac{1}{2} \text{H}_2\text{O}
\]
This means that for every molecule of calcium sulfate, half a molecule of water is attached. When Plaster of Paris is mixed with water, it forms a hard solid, making it useful for making casts and molds.
Thus, the correct formula for Plaster of Paris is \( \text{CaSO}_4 \cdot \text{H}_2\text{O} \), which is option (C).