Yes you can authorise a family member or a friend to sell your vehicle on behalf, however there is a few of things to take note of.
1. Ensure that you have obtained the Transaction-Pin from LTA before you leave the country and hand to the person authorised to assist in the sale. If not you can also request for the Transaction-Pin from www.onemotoring.com.sg and it will be delivered to your residential address.
2. Completed/Signed "Application Form For Transfer Of Vehicle (M01)". You can locate the form in the following link: http://www.onemotoring.com.sg/publish/onemotoring/en/lta_information_guidelines/forms_download0.MainPar.15985.collapsePar.67710.File.tmp/M01.pdf
3. Lastly you are required to get a "Power of Attorney" Letter to authorise the person to act on your behalf. Sample letter can be found in the following link:
Do note that the above is not applicable to a Company's Car. Different documentations will be required.