In a police report ... obtained by TMZ ... Mariah and Tom allege the first instance of harassment occurred in January. The couple told cops Daisy chased Tom in their neighborhood, got in his space, sniffed him, and declared her love for the TV personality.

Tom claims she would call out his name in the weeks following ... often inviting him inside for dinner. He says he was told by maintenance Daisy learned his name through his appearance on "90 Day Fiancé."

Tom alleges Daisy continued to appear wherever he was in the apartment complex for the next few weeks.

The report says Daisy also followed Mariah and Tom while they were out for a walk and repeatedly asked Tom if she could call him a Lyft or Uber -- an offer he declined.

Things allegedly escalated a few days later ... Tom claims Daisy chased Mariah and him out of their building as they made their way to their car and then got into Tom and Mariah's ride -- as the pair said they had unlocked their car in an attempt to escape the situation quickly.

Tom told officers Daisy rushed by the duo, jumped into the backseat and refused to leave for 20 minutes until officers were called to the scene. No arrests were made.

The couple says they eventually asked management to move them to a different building.