Municipal Water making my hair fall and frizzy

So I recently shifted and the land Lord mentioned there being municipal (BMC) water coming through the tap that's directly linked to the tank (which we need to fill two times a day during specific time slot), while the other taps get borewell water. Now, it's been two months and all of us have noticed that are hair is falling a lot more than before and is also extremely frizzy, which wasn't the case at our earlier home. I thought municipal water is not bad for hair? So why is this affecting our hair and how can we find a solution to this? Most softners available online are strictky for hard water, but municipal water is considered soft water.