For qualitative tests to work properly, you need a concentration sufficiently high to observe the effects, e.i. precipitation of heavy metal salts and/or color changes of solution. If heavy metals are present, they are likely to be in small concentrations (depending on how your water is filtered before it reaches your house).
If you are concerned about your water quality and want to check if heavy elements are present, you should contact a trustworthy laboratory that routinely analyzes water samples. They are likely to use trace-element techniques such as inductively coupled plasma mass spectrometry (ICP-MS) and ICP optical emission spectroscopy (ICP-OES), or maybe atomic absorption (AAS) techniques. This way you get accurate and precise quantitative measurements of almost all elements in the periodic table.