The state-by-state answer
Updated
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A method rather than a list, because a fifty-state table written once is a fifty-state table that is wrong within a year.
What to check per state
Business registration and sales tax. Every state, and the answer is on the secretary of state and revenue department sites.
Local business license. City or county, not state.
Home occupation rules. Zoning, and whether a business may operate from a residence.
Chemical disclosure or warning regimes. California is the well-known one; a handful of others have narrower programs.
Fire code at your premises, which is local and applies to storage quantities.
What you will not find
A candle license, a candle registration, or a state candle safety standard.
The product requirements are federal and voluntary, and they do not vary by state. Anyone telling you their state requires a candle permit is describing a general business license.
The four that come up
California, for Proposition 65 warnings, which attach to selling into the state rather than to being based there. Ask your fragrance supplier whether an oil contains anything listed.
Washington and a few others, for narrower chemical reporting programs that mostly affect children's products but are worth a check.
Any state you hold stock in, for fire code on stored quantities.
Your own, for the ordinary business registration.
How to keep it current
Check the state you are in annually and any state you sell into heavily.
The fragrance supplier is the most useful source for the disclosure question, because they know their own materials and they are asked constantly.