Matinecock officials have deferred a decision on a law that would permit them to override the state-imposed tax cap until they have a better sense of what their coming budget holds.
Leaders of neighboring Upper Brookville, meanwhile, passed a measure to pierce the cap on property tax levy increases if needed.
The two villages on Tuesday were the latest on the North Shore to hold public hearings on proposed tax cap laws that authorize them to exceed the 2 percent cap without incurring penalties.
This village budget season marks the second since Albany mandated the limit meant to reform and control spending.
Matinecock Mayor Kenneth Goodman said the village would "rather have permission in advance" to top the cap than pay penalties for doing so without the law in place.
The cost of cleanup after superstorm Sandy will likely factor into the budget calculations, as Matinecock has not yet been reimbursed by state and federal agencies, village attorney Peter MacKinnon said.
The village expects about $58,000 in reimbursement, or 80 percent of its Sandy cleanup costs.
The decision to adopt the law is to be made at the March or April meeting.
The village's final budget hearing is set for April, and its budget year begins June 1.
Other North Shore villages set to consider their own tax cap laws this month include Lattingtown and Brookville.