San Francisco’s “very fragmented system” presents an ongoing hurdle in The City providing on-demand behavioral health and substance-use treatment to residents who need it, public health officials said as part of a legally mandated annual progress report that one supervisor argues could also use rethinking.

The Department of Public Health presented the findings of its yearly “Treatment on Demand” report Thursday in a Board of Supervisors Public Safety and Neighborhood Services Committee hearing. Officials pointed to persistent — yet declining — drug overdose deaths and disconnected infrastructure as challenges to providing care as soon as someone needs it.

The department’s director, Daniel Tsai, acknowledged that there’s still a bit of “stickiness” in the process of moving people off the

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