If a city water line bursts and results in a flood to your property,  is there coverage under your homeowner policy for the damage?............No  it is not.
A flood can result from a water source other than storm and hurricane activity.   This type damage would also be covered with a flood policy. 
A flood is "A general and temporary condition of partial or complete inundation of two or more acres of normally dry land area or of two or more properties (at least one of which is your property)

Huffington Post Pictures - Tennessee Flood

"I DON'T NEED FLOOD INSURANCE.  I'm not in a flood zone."  While this is a common thought, EVERYONE is in a flood zone.  Some are considered lower risk than others, but FEMA reports 1 in 4 flood claims are from areas classified as low or moderate risk.  Even if you area hasn't flooded before, development in the past 10 years has the potential to change the landscape significantly and increase the amount of runoff.