New Hampshire - Bill Would End Requirement on Contraceptives Coverage Among Some Employers - NYTimes.com The Republican-dominated State House passed a bill on Wednesday that would exempt employers with religious objections from having to cover contraception for employees. The bill would change a state law, passed in 1999, requiring insurance companies to cover contraception. The House speaker, William O'Brien, sought such an exemption as a national debate erupted over a federal mandate for contraception coverage. The Senate is expected to take up the bill in April.