Rahim married Zabedah Abdullah and the couple have 4 children; Zetty Juyanty, Tutty Rahiza, Petty Diyana and Rahimy. Their eldest daughter, Zetty married the former TV3 personality, Kelvin Ong née Zahir Kelvin Ong Abdullah.
In 1994 Rahim was initially charged with statutory rape of an underaged girl; however, the public prosecutor later withdrew the charge citing lack of evidence. He resigned as chief minister of Malacca and youth chief of UMNO amid allegations he had sexual relations with the 15-year-old girl. In 1995, Democratic Action Party leader, Lim Guan Eng, who in the past had accused Rahim of raping the minor and had criticised the then-government for not acting against Rahim; was charged and sentenced to 18 months’ jail by the Melaka High Court for maliciously printing false news instead under the Printing Presses and Publications Act 1984 and under the Sedition Act 1948, but Lim was eventually released after 12 months. In 1999, Anwar Ibrahim in one of four police reports he made; Tun H.S.Lee report 22517/99 dated 20 August 1999 had accused that the Prime Minister then Mahathir Mohamed, attorney-general Mohtar Abdullah and Senior Deputy Public Prosecutor Gani Patail for abuse of power to cover-up the corruption case involving Rahim. A copy of the report was also sent to the Badan Pencegah Rasuah then. On 21 March 2011, Rahim was one of the 'Datuk T' trio; together with Datuk Shazryl Eskay Abdullah and Datuk Shuib Lazim who screened a sex video at Bilik Seri Makmur, Hotel Carcosa Seri Negara; claiming it was of the opposition leader then Anwar Ibrahim allegedly engaging a prostitute to journalists which Anwar had denied the allegation. On 24 June 2011, they were charged and fined by Kuala Lumpur Magistrate Court for screening the sex video after they pleaded guilty. Rahim was fined RM1,900 in default three months imprisonment by the Shah Alam Sessions Court on 20 September 2016, for making an offensive comment about Raja Muda of Selangor, Tengku Amir Shah on 25 September 2015. He also tendered a public apology to Selangor Ruler Sultan Sharafuddin Idris Shah and Tengku Amir, besides expressing remorse for his action. Rahim had earlier on 5 October 2015 claimed trial to an original charge of posting a seditious claim in his Facebook account that Tengku Amir was an apostate. However, the prosecution withdrew the charge after he pleaded guilty to the alternative charge.
