Power Supply Earth ground and power ground question

[RedAlert]

I would like to debug and repair boards at chip level. I usually use Lab Power supply and scope.
Usually it is common to supply the power to the board from the Red and Black power supply connector, but there is also Earth GND connector (colored Green)

When I use the scope to debug, then normally I connect the black lead of the probe to the board GND signal and probe tip to where I want to see the signal.
I do know that in the scope end the Earth GND and signal GND(I.E BNC GND) are connected together and would like to know if I can also connect the Earth GND to the Power GND in the Power supply unit (Green and Black connectors)? -If I do it then it will be possible for me to probe the signals without connecting the black lead of the probe to the board and it is neater and more comfort.

Actually I did that and it seem to work ok at least at measuring DC signals, but I would like to know if it is safe enough and common practice to do so?
I would like to emphasize that in the default state the scope Signal GND and Earth GND (I.E BNC ground and Earth GND) are connected and the lab power supply unit the Power GND and Earth GND (Black and Green connectors) are NOT connected.

Power supply used: http://www.mastechpowersupply.com/dc-power-supply/linear-power-supply/mastech-regulated-variable-dc-power-supply-hy3003d-30v-3a/prod_2.html

[pickit2]

as a general guide all grounds on equipment being tested, or calibrated, if mains feed then, thats the earth to reference to. Just added you also need to know if you have a floating ground.

one problem is you have to look out for earth loops, they will mess up any test signels. 

[RedAlert]

So, from you answer is it ok to connect the Ground and Green connector in the power supply and then off-course apply this to the board being examinated?
which ground are you referring to? there are two grounds - Earth GND and Signal GND and in the scope they are connected but they are not connected in the power supply, so If I connect them in the Power supply and apply this to the board being examinated it will be ok, common thing to do ?
The benefit I gain from this is that I won't need to connect the black wire (GND) of the scope.

Do you know how to check/test for earth loops?