Not likely, but there's a chance you might if you're in MD (the only state that does around here, assuming you live in the DCUM region).There's nothing at the federal level, but a handful of states tax inheritances.
https://turbotax.intuit.com/tax-tools/tax-tips/Taxes-101/What-are-Inheritance-Taxes-/INF14800.html
http://www.nolo.com/legal-encyclopedia/maryland-inheritance-tax.html
The fact that the distribution came from a trust instead of directly from an estate may change things. Though on further reading, it appears, in MD's case anyway, that the estate handles the payment before the funds are distributed.