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Testing for ecoli or other coliforms is unlikely to identify sludge leakage in this case. It will merely point out what is already fairly apparent that there is contamination in the water. This is most likely to originate from washing and laundry as well as animal faeces even if there is not human waste getting into the mix.
Basically I concur with the other answers, better take action to remove the problem rather than do a lot of analysis because if it isn't contaminated now it very soon will be.