You can always check your local government website for updates on the safety of tap water. Ignore some of the stupid comments here, you are very right to be questioning the quality of your tap water and it is good to be certain.
Sometimes it can depend what building you live in too. If you live in an old apartment block, old degrading pipes can pose risk to water quality too I believe. If you live near industrial buildings, gas stations, or other polluting buildings you may be more likely to have a lesser quality of water.
You can have water tested, there might even be do-it-yourself kits. Usually you can tell by color, smell, taste.
If you are concerned you can always buy a filter.
Its hard to suggest much, you should really research this yourself online. I'm sure there are lots of resources.