As far as I know, that start kit is not nearly enough.
First of all, you need to know what you'll be looking for, because for each kind of drug you'll need a kind of analysis: each substance affects the water in a very specific way.
My chemistry knowledge is pretty limited, and most I know nowadays I've been learning from my wife.
One such way of doing the analysis you want is through a spectrometer. This is one sensor that can interface with the arduino: http://myspectral.com
However, in order to analyze the data provided by the spectrometer, you'll have to know how each substance affects the water. You may need to have access to the substances in order to compare the results of "drugged" water against clean water and create a database from that. It is based in this database that the Arduino will know if the water being tested is clean or not, and, if not, what is the agent polluting it.
Keep in mind that a good spectrometer is pretty expensive. What it does is to break the light that goes through a substance and measure each wavelength of the broken spectrum (thus the name: spectrum + meter). Since substances in the water affects the way light goes through it, water with high levels of CO2 will give a much different spectrum of water with high levels of anthrax (for example). How these levels vary will be up to you do measure and create a database.
A more sure-proof analysis would be a chemical analysis, like the one done in labs with blood samples. They, however, not only do a chemical analysis, but they also use spectrometer. The kind of spectrometer they use, however, is called "real time PCR spectrometer" (or spectrophotometer), and it takes 1 uL (micro-liter) of prepared blood (with a UV reactant) to give you a very precise reading.