Test for chlorine and chloramine in city water supply
Test strips for chlorine should work for both chlorine- and chloramine-treated water. See Here-to-learn's comments to this answer for the chemical kinetic reason why chlorine test strips will also work for chloramine-treated water.

Notice that your city supplies the water with chloramine. Depending on how much chloramine is present in your tap water, leaving water to sit for days on the countertop would be necessary to remove a significant amount of chloramine.

Please see this research paper: http://hbd.org/ajdelange/Brewing_articles/BT_Chlorine.pdf

Page 17 estimates the half-lives of chlorine vs. chloramine.