Catskill bears have not yet learned to open cars the way bears out west have. So food in the car is safe. Make sure to keep all windows closed tight.
My experience at Woodland Valley is that the rangers take bear safety seriously, giving instructions when you check in and monitoring campers food storage. North/South Lake, on the other hand, had very lax bear policy when I was there. When we pulled into a site there last fall, the people across the way from us were running from their site from a mother bear and two cubs stealing their cooler. The rangers, who had given no bear instructions when we checked in, did not seem surprised or inclined to action when we reported this incident.
You're probably more likely to see a bear, a potentially aggressive one, at a campsite than off backpacking in the Catskills. So due caution is important.