If you need to measure the protective earth resistances then any meter designed for the task is suitable as long as it can provide a minimum of 200mA. In the UK we can use a Rigel or similar but as this is overkill. As the task is generally performed by electricians they use a standard electrical installation tester, such as a Metrel MI3125, Megger MFT170 or Fluke 1652c etc.
In the UK we don't to need to measure so called touch voltages (e.g. 10mV, 100mV) as this makes no sense. What you are trying to do is actually measure is leakage currents, so really you should be using a standard IEC 60601-1 human body model, as built into devices such as the Rigel 288. The question is why? Do you expect the electrical installation to be contacting the patient as an applied part? If so you would need to get the entire medical location tested as medical device!
If you just use a high impedance voltmeter to measure voltages between the earth reference and parts in the room you may measure high voltages, such as a automatic tap (faucet), which use a class II power supply. This could be as high as 110V but, if loaded by a 1K human body model, the voltage will collapse and you will get just a small leakage current (less than 250 micro amps).
One joke about the 10 and 100mV levels is a medical IT is allowed 0.5mA leakage so you would measure 500uA from this with a first fault to earth condition, so making a mockery of the lower two levels. Touch leakage and applied part leakage should be only of concern to medical devices and have nothing to do with the electrical installation. Here the proper equipotential bonding provides all the protection you need, when combined with RCDs and Medical IT systems.
