Indeed, some churches choose to file the form and have financial information recorded with the IRS; but the vast majority of churches never have to file any tax form.
See http://www.irs.gov/pub/irs-pdf/p1828.pdf for more information:
later on page 3:Congress has enacted special tax laws applicable to churches, religious organizations, and ministers in recognition of their unique status in American society and of their rights guaranteed by the First Amendment of the Constitution of the United States. Churches and religious organizations are generally exempt from income tax and receive other favorable treatment under the tax law; however, certain income of a church or religious organization may be subject to tax, such as income from an unrelated business.
What contract do you imagine a church might have with the government?Automatic Exemption for Churches
Churches that meet the requirements of IRC section 501(c)(3) are automatically considered tax exempt and are not required to apply for and obtain recognition of tax-exempt status from the IRS.
Although there is no requirement to do so, many churches seek recognition of tax-exempt status from the IRS because such recognition assures church leaders, members, and contributors that the church is recognized as exempt and qualifies for related tax benefits. For example, contributors to a church that has been recognized as tax exempt would know that their contributions generally are tax-deductible.