The incident Tuesday was the latest flare-up in an increasingly tense dispute between the Boston Police Department and the Massachusetts Department of Transportation over the use of civilian flaggers at city construction sites overseen by the state.

State officials say they want to use civilian flaggers, allowed under a new state law, to save money; police in Boston and elsewhere, who can earn huge amounts of money working at construction sites, have argued that public safety is better served by having officers, rather than civilians, working the jobs.