Stupid neighbor has problems with my dog

I live in a block of flats and i have a dog which is very quiet and nice.My neighbor always complains that my dog does her poops in my balconi and barks.Thats not true because i never leave her outside and i always take her out for walks. He told me that if i dont get rid of the dog he will start collecting signatures from other neighbors to evict me. The guy from whom i rent my appartement has no problems with my dog. What should i do???