The ruling Progressive Conservatives have been at the centre of controversy this week after the party said it had to cover $5,125 in rent for 2011-12 for Davis's office in his riding of Campbellton-Restigouche Centre.
A spokesman for the government said Davis later fell behind paying his rent again but did not say how much Davis owes.
Annual reports from the provincial comptroller's office say that Davis claimed his maximum allotment of $40,000 for constituency expenses in the fiscal years of 2011-12 and 2012-13.
Victor Boudreau, the Liberal deputy house leader, said the Tories should disclose how Davis spent money that was intended for constituency expenses.
"If the maximum was claimed and it didn't go to pay rent, where did it go?" Boudreau asked in the legislature.
"We're simply asking for clarity here to make sure that taxpayers dollars are being used in the proper way and that the Conservative party, if they did pay bills, that it was done within the rules as well."
Deputy premier Paul Robichaud did not say how the money was spent but told the legislature that health problems are to blame for Davis falling behind on his rent.
Robichaud said Davis's latest rent arrears would be resolved this week with the help of the legislature clerk, though he did not elaborate.
Clerk Donald Forestell confirmed his office was working to rectify the problem but would not reveal how much money is involved nor provide details of Davis's expense claims.
"We are working with the member to verify the matter, confirm rental costs, and fully expect to have it resolved before the end of the week," Forestell said in an email.
"Any funds to be paid by the legislative assembly with respect to a member's constituency office will first be verified as an eligible expense and must be funded from within the individual member's existing allotment."
Bob Fowlie, communications director for the government members' office, said later he was told that an arrangement has been worked out and Davis's office would reopen Monday. He said he did not know what that arrangement was.
Forestell did not return a subsequent request for comment.
J.P. Soucy, the executive director for the Tory party, said while an arrangement was made for Davis to repay the party for the 2011-12 rent arrears, it was not asked to cover his rent for 2012-13. Soucy said Davis is still reimbursing the party.
Davis, who has not been in the legislature since it resumed in February, issued a statement Tuesday saying he wouldn't run again in September's provincial election, citing unspecified health reasons.
He has not been available for comment.