I know this isn't what you asked for but it's important: is this on public land? If so, you should probably contact the land management agency and defer to them. In many cases, they want to be the ones to deal with the problem, not you.
If the above doesn't apply in this situation and you are the person who is supposed to be dealing with this issue:
It shouldn't matter whether you are using a static or dynamic rope because you shouldn't be loading the rope dynamically. Connect the rock to a rope and then just trundling normally it is a bad idea.
The goal is to have a controlled lowering of the rock. In this case the deciding factor for the rope should be strength. Is the rope strong enough to hold the boulder with a reasonable margin of safety?
If not, then get a thicker, stronger rope. Static ropes tend to be made of different materials and tend to have a higher breaking strength for the equivelent diameter or weight, but in this kind of situation, rope weight shouldn't very high on the priority list so just get a thicker rope if there is any doubt.