What type of sensor technologies exist to determine the chemical composition of a polymer?
You can identify many polymers without any clever sensor technologies at all but by following a number of simple physical tests. Sensor technology might help for some of the very fine distinctions, but if you can make a broad categorisation first with simple physical tests then that is what you should do.

And, of course, most plastic opponents are actually labelled with symbols to aid in recycling so you can often just look to identify the chemical nature of the polymer. For reference the symbols are shown below (V identifies chlorine-containing polymers like PVC):



The steps required to identify polymers, if you don't have a label, involve some simple physical tests. First identify whether the polymer is elastic or hard. Then identify whether it is a thermoplastic or a thermoset (by using a hot object like a soldering iron to see whether it remelts). Then a variety of tests can be applied: does it float in water or not? Does it burn and if so how does it behave and what does the flame look like?

One flowchart for this is available here as a pdf. Another simpler one is here also as a pdf but sufficient to distinguish the major classes of polymer. There are even interactive versions of such flowcharts such as this one (flash).

Included below is another version originally produced by the major, but now defunct, British chemical company ICI:



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