the best way to check it is lift both rear wheels off the ground, put the truck in Neutral, have somebody hold one wheel, and turn the other wheel. If it turns the drive shaft its not a posi.
Now the real question is "how much pressure does it take to make the posi clutches slip". I have heard as little as 35psi is OK in Dodges mind, but I can't find that thread so not 100% sure.
On my 2002, I was stopped on a hill, trying to go up the hill.
One set of rear wheels is on ice, and the other set is on dry and I hit the fuel, the one set will spin, but the posi will grab enough that the truck will also start to go forward.
Now if both wheels are "near" equal traction, they both will spin.
The rear builders have to come up with a compromise when building posi rears. If the clutches are to tight, the rear will cause one tire to squeal or feel like its skipping during dry traction turns, if its to loose it will let one wheel spin while standing still in low traction conditions.
Dodge will get more complaints from a rear that is to tight as you would feel it every time you turn, so they go on the loose side.
If you feel inclined, you can remove your posi carrier, and change the order of your clutch plates for more traction, at the expense of noise and strange feelings while turning in the dry.