What does "curb your dog" on a sign mean (exactly)?

Answers:
It means to please make your dog go pee and poop on/near the curb - as opposed to the middle of the sidewalk.

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Not positive, But I'm pretty sure it means keep your dog under control.

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I'm pretty sure it means keep them on a leash and under control at all times.

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clean up the dog's poop

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dont let your dog poop just anywhere, and dont let it run wild..

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tie it up

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it means to make the dog walk and * near the road side so when he craps someone doesnt mire it with a shoe sole and also so ths clean-ups can take place near the road and not in the [path - logic

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it really does mean to clean their poop i gotta do it

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it means don't let your dog go to the bathroom anywhere near where the sign is posted. it doesn't literally mean make them poop on the curb though lol. and always clean up after them :)

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I live in NYC, and see these EVERYWHERE.
They're usually on planters, and if dogs pee on planters, it kills the plants, so building managers are asking you not to let your dog pee on the plants/flowers, and to bring them to the curb (or just away) from the planters.
It's also just better/practical/polite to curb your dog than to let them pee/poop in the middle of the street or in a planter.

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control your dog, keep your dog on a very short leagh

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It means exactlly what it says. Walk your dog next to the curb and away from my property.