Price was already under fire from Senate Democrats for his extensive trading in health-care stocks, including Innate Immunotherapeutics, the Australian biotech company.
The memo, obtained by CNBC on Tuesday and first reported by CNN, said Finance Committee staff reviewed Price's answers to a questionnaire submitted to the panel, his tax returns for 2013, 2014 and 2015, and financial disclosure statements.
The memo said that when Price was asked if he had "ever been the subject of a complaint or been investigated, disciplined, or otherwise called for breach of ethics for unprofessional conduct" by a court, agency, professional association, disciplinary committee or other professional group, Price responded "No."
But in 2010, the Office of Congressional Ethics, which is an independent office of the House of Representatives, "conducted an investigation into Dr. Price's 2009 fundraising activities," according to the memo.
The committee voted 4-0, with one abstention, to refer the case to the House Ethics Committee. After doing a second investigation, that committee "found no wrongdoing," the memo said.
Price told Senate staff, when asked about the omission, that "it was an inadvertent omission and that the majority of activities investigated related to his authorized campaign committee, rather than him personally," according to the memo.
Separately, the memo said Price bought two blocks of shares in Innate Immunotherapeutics over the past two years: a relatively small tranche in 2015, and a larger tranche of more than 400,000 shares last August, in a private placement open to so-called sophisticated investors.
Price in a filing late last month valued the first block of shares at $10,000 "at the time of the purchase." But at the actual time of that filing, the shares had a market value $15,000 to $50,000, according to the memo.
The memo also noted that Price had reported in disclosure documents the second block of shares he had purchased were valued $50,000 to $100,000, "which was based upon the purchase price."
But Senate staff wrote that an analysis done by multiplying the number of shares by the market price on Dec. 20, 2016, "demonstrates a value higher than that reported by the nominee."
Price said the amounts that he had reported to the committee "were a good faith valuation." But he "agreed to recalculate the value of the shares based on the market value at the time the Committee Questionnaire was completed." The revised value of the second tranche of shares alone was was $100,000 to $250,000 at the time of the disclosure filing, according to the memo.
Price and the staff also agreed that the tranche of more than 400,000 shares had not been accounted for on an Office of Government Ethics form, according to the memo.
Price "noted that is is unclear how information related to his holding in this stock was misstated on the published form," and "agreed to contact OGE to correct the form," the memo said.