I agree with @SwirlyOfficeChair, almost entirely. I would add that you can get some sort of ballistics like where the shot came from based on wound channels etc, and possibly even an idea of range.
But like in algebra, you have a couple unknowns that you have to add together to get your answer (the blaster wound). Range, power, potency, etc.
If you know roughly what sort of weapon, you may be able to work out what range it was fired from based on how much energy/cohesion was lost by the blaster bolt before impact.
If you know roughly the range, you’ll be able to more precisely work out what sort of blaster because you’ll be able to deduce how much energy/cohesion was lost by the blaster bolt.
In that process, you may also discover some key distinguishing details like a very small loss in energy, indicating an unusually cohesive bolt generated by a particularly powerful rifle.
There would be various ways to deduce this, but here are the basics based on my understanding of blaster weapons:
What is the diameter:depth ratio of the wound? A powerful bolt is going to maintain a roughly even ratio to a weaker bolt, but a bolt that has lost cohesion will have larger burns and shallower penetration.
What was the explosive force of the impact? When a bolt impacts, it “compresses” until it builds up too much pressure and “explodes” (see my topic on the subject). The lack of such a micro-explosion or a very shallow micro-explosion is also very indicative of a loss of cohesion to where the bolt doesn’t maintain enough energy to cause such an effect.
Finally, different energy weapons are going to act in different ways. LRBs, auto-fire HBRs, and auto-pistols don’t fire a single, large bolt, but often multiple smaller bolts, their damage not coming so much from a single impact but from multiple smaller impacts. Someone riddled by an LRB is going to look very different than someone shot several times at point-blank range with a blaster pistol.
Additional factors:
The type of blaster gas also matters. If you arrive hours later, any smells or residue may have dissipated, but you may still be able to deduce what sort of blaster gas was used if you understand enough of the other factors. Different gases will have different cohesions, heats, power settings, and certainly smells. This can help you narrow down the results, though often not by much since it’s likely one of the most common sorts of blaster gas.
The main difference between slugthrowers and blasters, which makes it very difficult to perform ballistics testing on a blaster the way you would on a slugthrower, is that no physical projectile is left behind. There’s no rifling you can match, and no distinctive deformation on rounds fired by the weapon because the “round” disappears after hitting the target, and it’s “disappearance” isn’t a clue in and of itself like a disappearing bullet would be.
I think it would be difficult or even impossible absent special circumstances to get an exact match between a corpse and a specific blaster, but you can certainly narrow it down and “reconstruct the scene” as it were.
A note on automatic weapons in Star Wars:
My statement about multiple smaller bolts is not directly correlative to real life automatic weapons, which fire full-sized rounds (whatever size those rounds are) but have a very high cyclical fire rate, which means that the firing pin strikes, detonates the primer, and then the gases push back the bolt which picks up the next round, pushes it into the chamber, and then the firing pin clicks forward again, repeating the process. The ballistics do not really change, what changes is the controllability because of recoil.
Blasters operate on a different principle entirely, and my analysis is that a blaster’s rate of fire is limited by how fast it can “recharge” for the next shot. A light repeating blaster would shorten that sequence, sacrificing the power of individual bolts (to some extent) for a dramatic increase in the weapon’s rate of fire. Select fire weaponry would also grant semi-automatic modes that deliver more powerful bolts at the cost of a slower rate of fire. Baze Malbus’s “Staccato Lightning” blaster is a perfect example of this.