Submitting to Authority

Question for you all. I know that we are taught in the Scriptures to submit ourselves to all authorities over us (in Ephesians even). So, does that mean that we are to do anything that the authorities tell us – short of denying the Creator/Jesus? So, if the authorities – say your employer – tells you to lie, do you do it? If they tell you to sign a paper saying that you admit guilt for something you didn’t do, do you do it?

And if you don’t do it, are you sinning?