wat can i do about my dog being falsly accused of biting

It was my daughters birthday and i was bbqin in the back yard wen a guy came to the front of my house and started threatening my dogs life he said tht my dog bit his grandfather we told him it wasnt possible cause he was in the yard with me bbqin and trust me my dog sits patiently by the grill with hope of a droped peice of meat. then a ac officer came and he started pulling the ladies out of the house stating tht they were walking him by the store two blocks away wich isnt true either the officer then stated he would not write me a ticket.. two weeks later a ac officer came back to my house and wrote me a ticket this time he stated tht it happend right behind my house.. my dog is German shep and i got 6' fences with locked gates.do they have probable cause based on first officer reports