As you know, there aren't any laws protecting employee here in Singapore. The government is pro-business only. The only employees with some protection at all are those earning less than 2K/mo.
Having said that, there is nothing stopping them from requiring you furnish that information. If you don't furnish it, you can be perceived as trying to hide something - no job. If you do furnish it, they can possibly see what you actually think you are really worth. If you refuse to give it? Maybe no job offer?
When they ask for basic, that's exactly what it means. Basic Monthly Salary (the figure that they would compute your overtime or holiday or unpaid leave rate from). That means nothing included like meal, uniform, telecom, transport, AWS or any other type of allowance/bonus given. This is your gross monthly "salary' before CPF or any other deductions, statuatory or otherwise.
The risk of not furnishing it? No Job?
SOME PEOPLE TRY TO TURN BACK THEIR ODOMETERS. NOT ME. I WANT PEOPLE TO KNOW WHY I LOOK THIS WAY. I'VE TRAVELED A LONG WAY, AND SOME OF THE ROADS WEREN'T PAVED. ~ Will Rogers