Streisand's character, Judi Maxwell, makes a habit of stepping into the street without looking, causing traffic accidents. Apparently, Bogdanovich decided to add a fender-bender at short notice, when there were no stunt cars lined up. So he sent a crew member to a car rental agency, with instructions to get two cars with maximum collision insurance, filmed the scene, and then returned the wrecked vehicles.
*Jennifer, if you're reading this: Give up movies and run away with me! With your millions, I could easily keep you in the manner to which you've become accustomed.