I have a $32,000 gain on sale of rental property. If my income tax rate is 15% is this gain exempt from capital gains tax. What if the capital gain was 37k..

The maximum capital gain rates are determined by income level.  As example, your overall taxable income includes your long term capital gains (LTCG).

At the very least you'll have to recognize the depreciation recapture, taxed at ordinary tax rates.  But the mechanics of the calculation of capital gains doesn't mean "I'm in the 10% tax bracket - ignoring (LTCG) - so all my LTCG is tax-free."  As long as all your "other" income plus LTCG keeps you in the lowest two tax brackets your LTCG will be taxed at 0%.  But as soon as the sum of other income plus LTCG breaks through the upper limit of the 15% tax bracket, the excess will begin to be taxed at a 15% rate until the combined income reaches over $418,400, when the maximum LTCG is 20%.