I have two residences. One in Pennsylvania, the other in Ohio. How do I obtain dual residency?

"Dual residence" is sort of a misnomer, at least in regards to the several states of the U.S. You can only be a resident of one state at a time, for the purpose of voting. For other purposes, you also reside in one state or the other; but it will depend on the specific residency requirements for what your residence claim is (i.e: taxation, occupational licensing, college tuition, etc.)