This paper studies the contact stability and contact safety of a robotic intravascular cardiac catheter under blood flow disturbances while in contact with tissue surface. A probabilistic blood flow disturbance model, where the blood flow drag forces on the catheter body are approximated using a quasi-static model, is introduced. Using this blood flow disturbance model, probabilistic contact stability and contact safety metrics, employing a sample based representation of the blood flow velocity distribution, are proposed. Finally, the contact stability and contact safety of a MRI-actuated robotic catheter are analyzed using these models in a specific example scenario under left pulmonary inferior vein (LIV) blood flow disturbances.