HCTZ has some common, and serious side effects, hair loss is not one of them. If you experience hair loss you can report it to the FDA, for investigation of a new side effect.
In most descriptions of the drug side effects there is not much about hair loss but it would be logically understandable to assume that hair loss is a possible consequence of using a first line diuretic which reduces reabsorption of sodium. And as it is well-known a deficit of sodium causes hair loss.