Stormwater is often an suitable source of make-up for cooling towers. It can be of similar quality to river make-up water. It MAY even contain relatively "clean" water from undergound firewater system leaks, etc (wondered where all that water MAY be coming from when it isnt raining?). You MAY want to filter it to remove suspended solids. You will need to analyze it to see it's suitability... calcium, TSS, turbidity, silica, TSS, sulfphates, ammonia, COD, etc ... Beyond the scope here to define what cooling towers can tolerate (eg up to 1200 ppm Ca as CaCO3 is possible, 6000 to 10000 conductivity, etc), and it depends on your blowdown rates or cooling water to overall make-up water concentration ratios. Perhaps talk with your cooling water treatment vendor and work with them on the potential for a water re-use project!
Regarding bugs (microbiological activity), chlorinating the water as far upstream as possible should take care of that ... and good control in your recirculating cooling water. Of course, if the storm pond make-up water has lots of "bug food" in it (ammonia nitrogen, COD etc), it may require treatment or it may not be suitable for adding to cooling tower makeup.
Good luck.