Normally you would be liable for the vet bill. However, if your dog is leashed and under your control and the other dog is not leashed, then the other dog's owner has "unclean hands" and would likely be unable to compel you to pay for her vet bills.
This is not to be considered legal advice nor does an attorney-client relationship exist.
The general rule is that you are responsible for harm your animal causes. However, you set forth an encounter in which the other dog is allowed to run free in violation of the apartment rules while your dog is leashed. The other owner is clearly at fault for that breach, which will likely play a crucial role in the other dog having an encounter with yours.
Everyone has cell phones with cameras - photograph this woman letting her dog run free.
The foregoing is for general information purposes and does not establish an attorney-client relationship.
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