I agree with Antiphon. To expand a bit, as an EE who designs and builds and tests circuits, you should be very familiar with how PCB layout is done, with PCB layout design rules (and design-for-manufacturing guidelines). You should also be familiar with what things in a PCB design and fabrication can affect how well your circuits work.
You need to understand and be good at floorplanning the PCB layout (you should be doing that and giving it to the layout specialist as a starting point), with star-grounding any analog/digital/RF portions of the design, with characteristic impedance Zo considerations for high-speed designs, and so on. As the layout specialist is laying out the PCB based on your design and initial floorplan, you will get check plots at various stages where you will be looking at these kinds of layout issues. The better you are at working with the layout person, the better your design will work in the end.
In general, you need to specialize in PCB layout in order to do more complex layouts. You can certainly do small PCBs with simple layout software on your own. But once you get to a dozen or more ICs and multiple layers and smaller SMT geometries, that's when you want a dedicated layout person to be handling the layout tasks.
I've worked with both layout-only-specialists (they had no design experience), and with a very talented EE designer turned layout specialist. You have to spend a lot more time checking the details of the designs from a person like the former, but in the end you can get good results if you are careful. The advantage of working with the latter, is that he often can make helpful suggestions about part substitutions, he can sometimes catch design errors (not that that's ever happened to me...), etc.
BTW, with either type of layout person, your working relationship with them is very important. If you do not work well with them, your designs will suffer, the layout process will take longer, and there will be a lot of frustration and bad feelings. If you do some things to make sure that the working relationship is good, though, it goes a long way toward generating quality PCB designs that work the first time and have the fewest issues with them.
For example, we have a rule here that once I hand off my package to the layout person (that's the schematic, clean DRC file, BOM, Netlist and Floorplan), he "owns the token" for the design. I do not make any changes to the design when he has the "token". I can make a list for myself of things that I see that I want to change (like value changes for components, etc.), but I do not touch the source files while he is working on the layout. When he sends me back a check package, I can request the token back if I need to make changes, but you should strive not to keep throwing changes into a design while it is in layout. That indicates that you weren't careful enough, and sent the package off to layout too early. Changes mid-design can be very frustrating for the layout person, and are to be avoided if possible. Alternately, I sometimes tell my layout person what I need changed in the design, and they make the changes for me and continue with their layout. That's another advantage of my being able to use the EE-turned-layout person -- he is very good with the OrCAD schematic design software that we use here at my work.