Banks and mortgage holders take out that insurance when a homeowner misses a mortgage payment or fails to maintain coverage required by the mortgage.
Department Superintendent Benjamin Lawsky has said the high cost adds to struggling homeowners' debt, making it harder to avoid foreclosure.
The department plans to start hearings May 17 at its Manhattan offices. They're expected to continue two more days and will be webcast.
It has sent letters to 15 financial services companies directing them to provide testimony. That includes banks, mortgage servicers, insurance agents and brokers, insurers and reinsurers.