Last year, Kfar Vradim, another Jewish community in the Galilee, halted an auction for land for house-building after several plots were bought by Palestinian citizens.
Some 50 municipal rabbis issued an edict in 2010 against Jews renting or selling homes to Palestinian citizens.
And around the same time the deputy mayor of the city of Karmiel in the central Galilee was implicated in setting up a hotline for residents to inform on neighbours suspected of selling to Palestinian citizens.
Back at Afula's park, one man admitted to being a Palestinian citizen from the nearby village of Daburriya. Only giving his name as Abdullah, he said he had been employed by Afula as a park-keeper for four years. He declined to comment on the mayor's new policy.