As a rule, we recommend you hire a licensed contractor to do any type of building, plumbing, mechanical, or electric work AND you require them to make application for the required permits.  The person making application for the permit ultimately is the party responsible for making sure that work is compliant with the code, and that inspections are scheduled.
There will be times when you are going to hire multiple contractors for different phases of a project, for example, one person to do the framing, another to do the insulation, and yet another for the drywall.  In these instances, the contractors will not want to be responsible for the parts of the project that they are not doing.  In such a case it might be best for you to pull the permit.