With a few exceptions, the U.S. government doesn't have IP rights, so this data is available to anyone. And as you can see from a casual internet search, lots of companies have made businesses out of publicly available data, such as manta, and even this one, which gets lawyers and doctors' state licensing information to create profiles and encourages this Q&A interaction.
You do need to be mindful of a few things, such as misrepresenting that your directory is from the government, or from some other source, which could create trademark disputes, and such as using obsolete or inaccurate information, which would require the use of disclaimers and statements about no warranties being offered, etc.
You also have the task of choosing a viable and available trademarkable name and domain name for this service, which again raises trademark issues. As with launching any new business, your safest bet is to consult a lawyer before launch.
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With few exceptions, most U.S. Government and State records are freely available for use.
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Government records are, generally, not copyrighted.
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