The agenda for the City Council’s Finance Committee meeting at 8 p.m. Monday includes a discussion on whether to allot $10,000 for an independent investigation of Police Chief Thomas LaCroix’s arrest in Maynard last summer. Mayor Jeannette McCarthy asked for the funds, to be drawn from a Personnel Department account, after councilors tabled a request by the Police Department’s acting chief, Keith MacPherson, for $20,000 from free cash to conduct the inquiry. Councilors said they felt uncomfortable with the timing of the request. However, police officials have said an independent consultant should handle the investigation, citing an inherent conflict of interest if Waltham officers were to investigate the department’s ranking official, and McCarthy said LaCroix must be treated as any other officer would. McCarthy said in an e-mail to the council that she wants the city to pursue the investigation promptly after the conclusion of LaCroix’s trial, which is slated to begin March 27, so that a decision can be reached quickly on his status as chief. McCarthy may be called to Monday’s meeting to speak to committee members. LaCroix was suspended, on paid administrative leave, after his arrest on charges that he assaulted his wife and a female neighbor in Maynard in separate incidents last June.