When is a $2.3 million tax bill a relief? When it could have been worse.

The Massachusetts Supreme Judicial Court on Monday ruled that trusts managed by Bank of America Corp. on behalf of state residents could not avoid state taxes, especially if the bank’s local branches handled much of the administrative work.

The state’s highest court rejected an appeal by the Charlotte-based bank seeking tax refunds on behalf of some 34 trusts that it manages for Massachusetts residents. The bank had argued that since it was based in North Carolina, the trusts it managed didn’t have to pay Massachusetts taxes.

Yet the ruling clarified a previous decision by a state agency, finding that the taxes might eventually apply to a smaller number of trusts.

Big banks that do business in Massachusetts were concerned about the initial decision by the Massachusetts Appellate Tax Board, said Brad Papalardo, the director of government affairs and trust services for the Massachusetts Bankers Association.

The otherwise archaic tax refund case drew the attention of the state and national bankers’ associations. The tax board determined last year that as long as a bank had significant operations in the state, the trusts it managed could be taxed.

Bank of America, “is pleased that the court has narrowed the prior ruling, clarifying that this tax can be imposed on a trust only if a material amount of trust administration occurs in Massachusetts for the trust in question,’’ said Bill Halldin, a bank spokesman.

The case arose in 2011 when Bank of America asked the state’s Commissioner of Revenue for a $2.3 million refund for the taxes paid by 34 trusts in 2007.

Papalardo said the state high court decision means that the Massachusetts tax commissioner will have to look at each trust being taxed and where the administrative work is done individually.

“We’re pleased with the decision,’’ he said. “The main thing is that we get clarity.’’

Deirdre Fernandes can be reached at deirdre.fernandes@globe.com. Follow her on Twitter @fernandesglobe.