Cats do have a preference. Here's something I found about doing an experiment to determine which paw a cat prefers.
This is a good research question. Scientists have found that some animals really do have a preference for one hand over the other. Like humans, monkeys, apes, mice, and gerbils all have preferences for one hand. Even some fish seem to prefer a particular fin for certain behaviors. Here's how you might test your hypothesis: Cats often reach for an object that is placed just a bit in front of them. You can use this natural behavior to study whether cats tend to reach more often with their left or right paws. Try placing a stuffed mouse or catnip toy just out of reach of the cat. To make the cat reach at the toy, try slowly pulling the toy away from the cat just a bit. Cats love this! Next, record whether the cat reached with his left or right paw. Repeat this as many times as the cat will tolerate your teasing! You should try to get the cat to reach about 20-30 times so that you can accurately determine whether he has a preference.
You should try to test as many cats as you can. That way, you'll be able to begin to see whether cats as a group have a general tendency toward preferring right or left paws. Posted By: Lori Holt, Graduate (Ph.D.) Student, Psychology, Ph.D., University of Wisconsin Date: Thu Sep 11, 1997
From Cats International website: Out of every 100 cats approximately 40 are left-pawed, 20 are right-pawed, and 40 are ambidextrous. These findings contrast strikingly with the human situation where only 10 individuals are left-handed for every 90 who are right-handed.