It depends on how "kennel" is defined in the zoning by-laws. Typically on Cape Cod it means commercial kennels, where boarding for dogs owned by others is offered for payment, as opposed to for use by homeowner with only one or two dogs.
Ask Town Planner, Daniel Fortier.
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Another thing to look for if under the chart is whether the use is an "N" or an "SP". If an N, meaning no, and the operation meets the definition Atty. Molloy describes, no it can't, unless the use pre-dates the zoning and is thus grandfathered. If an SP use, it could be allowed by obtaining a special permit from either your Planning Board or Zoning Board, which would have had to find after a public hearing with notice to abutters that the use was not substantially more detrimental to the neighborhood .
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Agree with Ms. Molloy and Mr. Cavanaugh and would offer a third "exception" to the "no" answer your question implies: is this a "prior non-conforming use" which antedates the zoning ordinance iteself or the changes in allowable uses in R-40 to prohibit kennels entirely or only with a "Special Permit"?
If so, the use can usually continue because of longstanding zoning and constitutional legal doctrines (e.g., prohibiting "ex post facto" laws or governmental "takings" of private property for public use without just compensation).
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