You don't need to pull the pumkin
If you know whether it's a limited slip, or if you don't...........
Jack up one wheel with the wheels safely blocked, put the trans in neutral. Parking brake of course released
If you can turn the tire, it is not a limited slip
Watch the driveshaft and turn the tire TWO turns while counting driveshaft turns. The driveshaft turns will BE the ratio IE turn tire TWICE, shaft turns "about 4 1/10," you have 4.11/ 4.10, etc
If you can NOT turn the one tire, jack up BOTH rear tires, and turn either of them 1 turn instead of two and again count shaft turns, same deal as before
For "increased accuracy" turn the one tire 20 turns or 10 and divide accordingly