Cate, this is really a gray area. Singapore law really hasn't caught up with the idea of telecommuting. and there are two things to be looked at.
A - Do you need a work permit?
The answer to this question appears to be "no". You are not working in Singapore. You are not in competition with any Singaporean for a local job. You are not working for a local company. So far as I can tell, you couldn't apply for a work permit because there is no company that would be submitted it.
The Singapore company must be a different legal entity... it is a Singapore company, not a USA one. It is probably a wholly owned private limited. If you were working for this company, you would need a work permit and would pay Singapore personal income tax, even if your salary came from the USA corporation.
B - Do you need to pay income tax?
Income that is foreign sourced is not subject to tax. The question is whether or not the work you do for the USA employer is subject to Singapore income tax. At
http://www.iras.gov.sg/irasHome/page04.aspx?id=13826, the statement is made,
"The service income is considered foreign-sourced if the services are provided through a fixed place of operation in a foreign country. A fixed place of operation refers to a place of management, an office or some floor space where the taxpayer or its employees provide the services. "
So, by telecommuting, are you providing services at a fixed place of operation in a foreign country? Although I've not seen anything specific about this, I think the answer is "yes" because you provide your HR services at the USA company, even though you have emailed them in from Singapore. You may have access to company servers located in the USA.
If you are intending on contracting, the situation becomes much more murky. You don't work for the company, you work for yourself. You don't have an operation in a foreign country, your operation is here in Singapore. The same page says,
"The service income is considered Singapore-sourced and taxable if:
• The services are not provided through a fixed place of operation in the foreign country and;
• One is carrying on a trade, business or profession of providing such a service in Singapore."
In summary, I believe you don't need a work permit and if you are contracting to the USA firm, which you implied with your original question, then you will be liable for personal income tax in Singapore.
The alternative is to create your own company here, and go to work for it. Not an Entrepass. Several professionals have gone this route and there are a few threads on this subject in the Careers forum.
For more information on tax exemptions for foreign sourced service income see:
http://www.iras.gov.sg/irasHome/uploade ... Income.pdf
Your best bet is to call IRAS to determine if you are taxable based upon your circumstances.