It looks like they did, according to this article:
"North Port PD had cameras set up around the Laundrie family home but that strategy was not successful. Those who were watching the Laundrie house saw Brian leave in his grey Mustang. They then thought they saw him return days later, but they had mixed up Brian and his mom.
Taylor says North Port police began tracking Brian after his fiance’s, Gabby Petito, family reported her missing in the State of New York. They reported her missing on Saturday, September 11.
Police then watched him leave in his Mustang on Monday, September 13 and he returned on Wednesday, September 15."
North Port police admit to mistakes in Brian Laundrie investigation