The 4-3 vote was a rare show of partisanship on the board, with the board's Democrats approving the concept and the Republicans holding out for more information from the county.
The resolution passed after a motion to table it was defeated in another 4-3, party-line vote.
Board President Baird Standish, who voted with the majority, said the resolution approved only the concept of using township property for the so-called Flourtown Connector, which will link two sections of the Wissahickon Trail.
The township would still need more information from the county regardless of the outcome of the vote, and he would vote to reject a trail agreement if it did not address residents' concerns over privacy, Standish said.
"I want to see how this plays out," he said.