Photoshop: Duplicated layer distorts

Your question implies that you print an image, crop it and print that and then have two sheets of paper you are trying to align accurately. 


If that is the case, you might not have a Photoshop problem and might be a victim of something your printer is doing, such as optimising the fit on the page.  Generally, one of many benefits of Photoshop is that it can position images to the nearest pixel.  Although modern printers are good, they provide relative precision, not absolute precision.  For example, I often need to print business cards, and for many weeks, I nearly drove myself nuts trying to print right up to but not past the perforation separating each card.  The cards and/or printer won that squabble.  Some business card stationery has a gutter, allowing the trick of printing a border or background into the gutter.  Alternatively, I just leave a substantial margin to produce attractive results. 

In your case, maybe your solution is to do more of the assembly in Photoshop, so that when the time comes to print, you print just one sheet of paper, with everything aligned perfectly. 

Conversely, the word "crop" is a clue.  This implies that the size of something has changed, so maybe a change of size in your printed output is just the result that should be expected from cropping the image. 

Thanks for your reply. Yes, I'm aligning two pieces of paper. This part of my art process. The printer interface tells me that no change in scale is made. No "scale to fit media." When I crop I'm simply removing unwanted pixels. No scale change here either. I should simply be taking a piece of the larger image and duplicating it exactly. I have not been able to discover any place that I'm introducing distortion or scale change. 
I don't wnat to do more in PS because part of the point of the process is to collage multiple pieces of paper. If you're interested, I can point you to my website for examples.