Q:

Does the power supply needs to be isolated from the earth for this circuit?

The following circuit is a discrete topology I have implemented on a strip-board to obtain +/-12V split supply from a regulated 24V single supply(V1 in the schematics):

Now V1 is not battery but a power supply SMPS or most likely a lab power supply. I want to observe the split voltages +V and -V by using a scope.
My question is does this way of split supply requires any precaution? Does V1's negative terminal needs to be isolated from the earth ground? In my case both the lab supply(V1) and the scope will be earth grounded. Am I violating something here? It seems to me V1 should not be earth grounded. Is there any other precautions for this circuitry? 

A:

In my case both the lab supply(V1) and the scope will be earth
  grounded. Am I violating something here?

Yes, you are violating something. More specifically, if you connect the common node of R3 and R4 to ground AND V1 negative terminal is also connected to ground, you create a short circuit and quite possibly a little bit of noxious smoke.

