Arduino GND and +5V connected

Today I wanted to be super safe and check all connections on my circuit if there are some shorts. To my horror GND and +5V seemed to be connected - and I couldn't figure what I did wrong.

I removed the Arduino (Nano) from the circuit - and the short was gone!

Then I checked a bare Arduino Nano (and also a Uno). Same result - connected (means: resistance between pin GND and pin +5V is only about 1200 Ohm).

Why's that?

1200 ohm is reasonable. You've got a regulator, 328P, FT232, all will show some resistance between power & gnd with paths thru transistors & diodes.

Of course it is. If it weren't you would not be able to make a complete circuit. All circuits are loops. You must be able to start at one point and trace all the way around back to the starting point or the circuit will not work.

What you are measuring tells you that with 5 V in you can expect about 4 mA to flow, if all else stays the same. How much does your arduino use when powered with 5V instead of just the test signal off the multimeter ?