I am actually dual-trained and this has happened quite a few times and has caused some quarrels between the Chef and the Restaurant Manager. I am not exactly sure what the law says about this, but this is how its handled with me.
At the point of hitting 40 hours, I am compensated for OT from that point on until the end of the pay period regardless of what department I'm currently in. I have been paid OT from both departments in the same week.
If my first 5 shifts of the week are 8 hour FOH shifts, and the next day I am scheduled to work in the kitchen, I am paid OT for working in the kitchen because I reached my 40 hours already in FOH. Vice versa also. If I am scheduled to work 40 hours in the kitchen, and I pick up a serving shift the day after 40 hrs, I am paid OT on server pay (which isn't that big an issue since they don't get paid as much).
If i pick up a serving shift in the middle of the week. So say 8 kitchen hours on Monday, 8 Tuesday, 8 Wednesday, 5 FOH hours Wednesday night because a server called off, 8 kitchen hours Thursday, and 8 kitchen hours Friday. I would be compensated for 5 hours of OT kitchen pay on Friday because the 5 FOH hours I picked up made me hit my 40 mark earlier.
Sorry if its confusing, I tried to explain it. And yes, as you can imagine, Chef was not happy to see me getting so much OT when I was serving alot. Now that I am 95% back to the kitchen, he doesn't seem to mind me getting OT as much.