It depends on the State. In some states, sales taxes are considered "excise taxes" and are dischargeable. In most states including New York, sales taxes are "trust fund taxes" and NOT dischargeable.
Further to what Atty Schwartz has said, sales taxes are typically "trust fund" taxes that a vendor collects from the purchaser and holds "in trust" to pay to the state. If you collected the sales taxes from your customers, I'm sure you understand why you can't discharge your obligation to pay them over to the state. If you did NOT collect taxes when you should have, your remedy is to seek an abatement of the tax. You would need to retain someone who specializes in NY sales tax issues to help you with that.
When you collect taxes for a govenement entity, that is referred to as "trust fund" taxes. If instead of remiitting those trust fund taxes you do something else with that money, that debt is not generally dischareable in bankruptcy.
"Sales Tax" can be taxes
That you owe on a purchase you made (a car purchase, for example), or taxes that you, as a vendor/Seller were required to collect and turnover.
In NYS the answer is no, sales tax is not dischargeable. However, sales tax is dischargeable in some other jurisdictions, so you will want to check with a local attorney.
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In NY Sales Tax are not dischargeable. Sales tax are considered trust funds in favor of the government. These are taxes you collect from the purchaser and hold in trust to pay the state.