Can the contractor apply for the permit on my behalf?

For bathroom remodeling.

In NYC for bathroom remodeling you don’t need a permit unless you are changing the dimensions of the bathroom but yes Conctractors can always apply for permits on your behalf

Pav

Yes, in most states this is common practice. Many communities/towns/city/county etc. require contractors to carry certain license and insurance. This gives the consumer an added layer of protection and this also usually activates the inspection process to ensure your contractor is following appropriate building codes.

If you hire a contractor—yes–you will sign statements to such, permit application or N.O.C.

In California you can pull the permit yourself as the owner/builder or you can have the contractor pull the permits on your behalf (recommended) and be responsible for the permit getting finalized.