On 30 June, the trust reported a year to-date deficit of Â£738,000 compared to a planned shortfall of Â£125,000.
Monitor said the trust's "finances will continue to deteriorate" and is yet to decide on whether further regulatory action is needed.
The BCPFT said its finances were its "biggest challenge".
Karen Dowman, chief executive of the trust, said: "We have already started a programme of activity to identify cost-savings and improve our financial sustainability, and to put in place safeguarding checks to ensure efficiencies do not compromise care."
Marianne Loynes, regional director at Monitor, said: "No decision has been taken about whether further regulatory action is required and an announcement about the outcome of the investigation will be made in due course."
The trust provides mental health, learning disability and community healthcare services across Sandwell, Dudley, Walsall and Wolverhampton.

But the Labour-controlled authority, which says it must save £200m by 2018, also confirmed up to 1,600 job losses.
Approving the council's budget for the next year, leader Simon Henig said "extremely difficult decisions" still had to be made.
Planned cuts to adult care, school transport, refuse collections and libraries will go ahead.
The council, which employs about 10,000 people, said cuts in government funding meant that initial forecasts of a total reduction of 28% to the budget were now more likely to equate to 36% up until 2018.
Savings of £90m have already been identified and a extended public consultation will hope highlight further areas for savings.
Mr Henig, said: "Our recent consultation shows a high level of understanding of how we have managed spending reductions so far.
"However, there is no doubt there are many more extremely difficult decisions which we will have to make. We will make these while continuing our discussions with residents and businesses in the county and while protecting those who are most vulnerable as best we can."

The Chelsea skipper is alleged to have made racist comments towards Queens Park Rangers defender Anton Ferdinand in a league match on 23 October 2011.
A not guilty plea was entered on Mr Terry's behalf at Westminster Magistrates' Court on Wednesday.
He will now stand trial on 9 July, nine days after Euro 2012.
The Crown Prosecution Service (CPS) said Mr Terry, 31, is accused of a racially-aggravated public order offence.
Following Wednesday's hearing, the footballer's legal team said in a statement: "Mr Terry looks forward to the opportunity to clear his name.
By Dan RoanBBC Sports News Correspondent
The fact that Terry will not stand trial until July means he is now free to lead England into the European Championship, the Football Association, along with Chelsea, having made clear it will not suspend him.
However, it also means these serious charges will hang over him for a further five months.
Terry says he does not wish to talk about the case, but you can be sure he will be asked.
Some will worry about the effect this uncertainty will have over on his performances in the summer and the England team's morale.
"Mr Terry denies making any racist statement and will establish in court that he is not guilty of any such offence.
"Mr Terry has never racially abused another player in his entire career.''
Police questioned Mr Terry under caution in November and a file on the matter was sent to the CPS at the beginning of December.
The decision to charge Mr Terry was taken after police received a complaint from a member of the public after the Premier League match at Loftus Road.
The maximum sentence for the offence is a fine of £2,500.
As a summary offence under the Crime and Disorder Act, it will be fully heard in a magistrates' court.
The Black Country Partnership NHS Foundation Trust (BCPFT) is being investigated by a health regulator due to concerns over its finances.
[NEXT_CONCEPT]
Durham county councillors have agreed to freeze Council Tax for the fourth consecutive year.
[NEXT_CONCEPT]
England football captain John Terry will stand trial for alleged racist abuse in July, after the final of the European Championship in July.