I had not experienced with this but one of my friends had experienced the same problem. Being a Singapore Permanent Resident is one of the most important steps to immigrate to Singapore as a resident, Singapore do not give citizenship by birth. If mummy is Singaporean, daddy is Malaysian, baby born in Singapore will hold Singapore Citizenship. It is because the Singapore birth cert will state Baby is a citizen of Singapore at time of birth. So Malaysia will not give out citizenship application form (borang W) for you to apply your baby as Malaysian. The steps for proceeding to have Singapore birth cert are as follows:
Apply Singapore birth cert. Can be done at Hospital or at Singapore Immigration at Lavendar by these simple steps:
-> Apply Malaysian Borang W by bringing baby to stamp Passport Application Form at Passport counter but submit 1 week later when Borang W is ready.
->Upon collection of Borang W, apply for Malaysian passport
-> Upon collection of Malaysian passport, apply Singapore PR