If your girlfriend is staying at your house temporarily, you do not need to register her details with HDB as she is not a tenant.
However, you must do your due diligence by checking her original NRIC or FINS 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, you 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.
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(CEA Reg No: R063413E)