The total income on the tax return will be a factor on the amount you owe. The pension taxable portion for the federal return will depend on whether you contributed any money to the police pension that was 'after tax'. If not, then it will be fully taxable on the federal return. The total taxable income on the return determines your tax rate.
Example: If your taxable income on the return (line 15, Form 1040) is $30,000 your tax rate would be 10% (approximate). This would mean $3000 tax liability. The withholding rate on your pension is approximately 4.3%. You may want to consider completing a new W-4P for your pension withholding.
For New Jersey, they have a Retirement/Pension Exclusion. You can review more about this by visiting NJ Form 1040-2020 Instructions, page 19.
TurboTax will walk you through it.
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