Brookline is going to sit on an order to remove numerous fliers posted around town for author Dennis Lehane’s missing dog, Tessa. Town Administrator Melvin Kleckner said in an e-mail Friday night that, with an offer by the Animal Rescue League to facilitate, he’s directed Brookline’s Department of Public Works to hold off on taking down the signs “in the hopes that a more coordinated and reasonable approach on posting signs can be worked out.’’ In a statement Friday, Lehane had said he would comply with an earlier request by the town that the Tessa fliers be taken down. “I can see the town of Brookline’s point,’’ Lehane said. “And there’s no reason we should expect preferential treatment because of my last name.’’ Lehane, the author of New York Times bestseller “Mystic River’’ has been posting signs all over Coolidge Corner and Brookline Village since his 4-year-old beagle jumped a fence on Christmas Eve and went missing. Lehane has offered to name a character in his next book after whoever finds the dog. Tips have been posted on his Facebook page, Finding Tessa. Several residents were left howling mad when the town initially said the fliers had to come down. “Where are our priorities when people are doing the right thing?,’’ wrote Sharon McHugh, one of dozens of commenters. Lehane said Brookline and Boston have been nothing but supportive during the search and he thanks them wholeheartedly.