You can rent a private property for three consecutive months but not an HDB flat as the minimum rental period is 6 months per application.
All types of private residential property are subjected to an occupancy cap of six unrelated persons per property. Unrelated persons refer to anyone who is not part of the same family unit. Domestic helpers are considered part of the same family unit. The occupancy cap also applies to tenants who sublet the property.
A landlord is required to check original NRIC or FINS of the tenants and occupiers for forgery and make copies, check photographs on NRICs or FINS against the actual persons to confirm identity and verify the validity of the passes with MOM database and/or ICA database. As an added due diligence, they may also ask for letter of employment from employer. This is to deter illegal immigrants or vice activities. This is required by the Council of Estate Agencies for compliance with the Immigration and Women's Charter.
Hope this answers your question.