How do I determine whether a permit is required for a new gas line?
You would need to find out who the authority having jurisdiction is. Often time, it is the city, county, or township where you are located. In some cases, it might be the state as well (in MN for electrical, for example).

The wording is a little ambiguous, however. They could mean:


You (the owner) pull the permit, but put down that the contractor is doing the work. This is not unheard of and probably fine. The contractor may be small and not want to deal with pulling the permit. This will then also indicate to you whether they are (or need to be) licensed to work where you are.
They want you to pull a permit as if you as the owner were performing the work. Do not do this. In this case, if something goes wrong with the job, you would be the one responsible for it. For example, after the work is done, the inspection reveals some issues that needs to be addressed. Do you think the contractor will not come and fix it if they've already been paid? Probably not. This scenario could also lead to issues when you sell the house.