If a petition to establish, modify the boundaries, or dissolve a county rail district is filed with the county legislative authority that complies with the requirements specified in RCW 36.60.110, the legislative authority may accept the petition, fix a date for a public hearing, and publish notice of the hearing in one issue of the official county newspaper. The notice shall also be posted in three public places within the area proposed for establishment, modification, or dissolution, and shall specify the time and place of hearing. The expense of publication and posting of the notice shall be paid by the signers of the petition.