Typically, if the third party vendor is in the course of performing services and they negligently injure themselves or someone else, or they cause property damage, then they will be responsible. Your contract for these services should spell out who is responsible and it's common to include an indemnity clause wherein the vendor expressly agrees to hold you and your business harmless for any injury or damage they cause. However, if there is some unreasonably dangerous condition at your business that you haven't warned them about and they are injured as a result, or if you retain control over how they perform their services (i.e.: dictating the manner in which they work and the materials they use), then you may also be liable for injuries they sustain or cause to someone else.