The simplest idea would be to save the initial angles and positions of each part of the ragdoll and rotate and move each piece toward those initials when you want it to reset. You may even be able to get away with only using the initial angle. Here's the idea. You can replace the "every tick" with a condition to reset the ragdoll.
Start of layout:
--- sprite: set initialAngle to self.angle
--- sprite: rotate 100*dt degrees toward self.initialAngle
A slightly more deluxe idea would be to save the initial angle difference between each body part and the other part it's connected to. It would probably give a more natural motion I imagine.