So your tenant paid a utility bill and you agree to reimburse the tenant?
I would simply give them a discount on their next month's rent. You would not report the expense as an expense you paid, you just report the lower amount of rent as income. That has the same effect on your taxes and is simpler.
(In other words, suppose the rent was $1000 per month and the utility bill was $300. Whether you report $12,000 of rental income and a $300 expense, or simply report $11,700 of rental income, your tax position is the same.)
