PCR testing is free regardless of insurance or immigration status. When you give your insurance information, it allows the laboratory to bill your insurance to get reimbursed for the cost of the tests.
Since the passage of the Families First Coronavirus Response Act (FFCRA) on March 18, most people should not face costs for the COVID-19 test or associated costs. Starting on March 18 and lasting for the duration of the public health emergency, all forms of public and private insurance, including self-funded plans, must now cover FDA-approved COVID-19 tests and costs associated with diagnostic testing with no cost-sharing, as long as the test is deemed medically appropriate by an attending health care provider.
For more information please see this Heath Affairs article