We prove decidability for contextual equivalence of the λμν-calculus, that is the simply-typed call-by-value λμ-calculus equipped with booleans and fresh name creation, with contexts taken in λμref, that is λμν-calculus extended with higher-order references. The proof exploits a labelled transition system capturing the interactions between λμν programs and λμref contexts. The induced bisimulation equivalence is characterized as the equality of certain trees, inspired by the work of Lassen. Since these trees are computable and finite, decidability follows. Bisimulation coincides also with trace equivalence, which in turn coincides with contextual equivalence.