Boston police say there is no way to guarantee overtime savings sought by Janey By Danny McDonald Globe Staff,Updated May 10, 2021, 6:43 p.m. Email to a Friend Boston police headquartersDavid L. Ryan/Globe Staff/file With city authorities looking to rein in Boston police overtime costs, department brass told lawmakers Monday that they could not guarantee the desired savings in next fiscal yearâs budget because injuries to officers â which require overtime shifts to fill â cannot be predicted. Boston police chronically exceed their annual overtime budget. During a virtual budget hearing on Monday, Boston City Council members pressed for tangible and structural ways for the department, which has been hit hard by COVID-19, to curb spending. Acting Mayor Kim Janeyâs $3.75 billion operating budget includes a projected $22 million cut to police overtime, or roughly a one-third