someone is claiming my dog broke their dogs leg. Am i Liable for tthe damage?

If your dog has no history of aggressive behavior, then you had no reason to think he would harm the other dog and therefore it does not sound like you did anything negligent.  It also seems like there is some assumption of the risk when they invite other animals onto their property.  There is also the question of whether your dog even caused the injury and I don't know what proof they have of that.  So it sounds as if they will have a very hard time proving their case, should they choose to take legal action against you. This answer is given in accordance with the laws of Virginia and may not be applicable in any other state.  It should not be construed as legal advice, as that would require a more thorough analysis of all of the facts involved in a specific case.  If you need further information or assistance, please feel free to contact my office for a consultation. Case results depend upon a variety of factors unique to each case. Case results do not guarantee or predict a similar result in any future case.