I was overpaid on my recent paycheck by an amount that bumped me up to a higher tax bracket. My company wants me to pay them back the net overpayment but now my check is lower than it would have been should I have been taxed in my correct bracket? How should I proceed?
You could claim the excess tax paid as refund while filing the tax return. It is easiest to pay back by deducting the excess amount from the next month's salary since this means that your total annual salary is automatically corrected. If this cannot be done, you should obtain a suitable "receipt" from your company, which your tax department will accept.
Tax rules vary by location, but usually the entire income does not get taxed at the highest tax bracket rate. Instead only the income above the upper limit of next lower tax bracket gets taxed at that rate. To illustrate with an (oversimplified) example, consider the below tax brackets:
$0 - $100 ==> 10% $100 - $500 ==> 20% $500 - ==> 30%
If you income is $400, then your tax is:
10% x $100 + 20% x ($400 - $100) = $70
If you were paid $600 in error, your tax becomes:
10% x $100 + 20% x ($500 - $100) + 30% x ($600 - $500) = $105
You could thus pay back $200 to the company, and claim a refund of $35 in your tax return. Unless the tax department pays you a substantial interest on the excess tax paid, you will still end up making some loss.
Unless the amount is excessive (they paid $48,829.50 instead of $4,882.95) a reasonable company would inform you about the error, pay you less the next month, and your tax would be adjusted automatically. The only difference is if you had the excess payment in the last month of the tax year, where you would arrange with them to pay back the excess within that tax year.
Moving into another tax bracket will in most countries have very little effect on your taxes in most cases. The higher tax rate usually only applies to the amount in the higher tax bracket. And if you file a tax return, everything will be sorted out anyway.