Concept:
The Double-Mass Curve Method is used to check the consistency of rainfall records at a station.
It compares the cumulative rainfall at the station under consideration with the cumulative average rainfall of surrounding stations.
A change in the slope of the double-mass curve indicates inconsistency in the recorded rainfall data.
Step 1: Understand the double-mass curve method.
The cumulative rainfall of the station is plotted against the cumulative average rainfall of neighbouring stations.
If the graph is a straight line,
\[
\boxed{\text{Rainfall data are consistent}.}
\]
If the slope changes,
\[
\boxed{\text{Rainfall data are inconsistent}.}
\]
Step 2: Identify the correct method.
Hence, the consistency of rainfall data is checked by the
\[
\boxed{\text{Double-mass curve method}.}
\]
Therefore, the correct option is
\[
\boxed{(C)\;\text{Double-mass curve method}.}
\]