Is there a correlation between hot springs and earthquakes?
Yes, there is a correlation.

In other words: places with hot springs are more likely to experience earthquakes than places without hot springs. The relationship is scale-dependent in time and space (your house might not sit on a hot spring but still get earthquakes). 

Ideally I'd dig around and find actual data to quantify this spatial correlation (and I hope someone does!), but for now I will settle for qualitative evidence at the continental scale. I offer a visual correlation between the two datasets in question. First, geothermal springs:



Now earthquakes:



Like any correlation in geoscience, it's not perfect. But, broadly speaking, there is one.

Footnote: Actually, there are at least two correlations. As with fracking for shale gas, well stimulations and other industrial activity in geothermal fields has recently been blamed for induced seismicity in places like the Imperial Valley of southern California. Sometimes correlation does imply causation!