In NJ one of my coworkers do not show any state tax deductions on any of her pay stubs so how is it that she does't have to pay state taxes in NJ.

Off-hand, I can think of two reasons:

1) Due to NOT owing NJ taxes in 2008, she requested and received an exemption from NJ tax withholding. In other words, if she knows she will NOT owe any NJ state income tax for 2009, why have the money withheld to begin with.

2) She screwed up and failed to have her employer withhold the money, in which case she will write a substantial check to NJ come 15 April 2010, plus under-payment penalties.

It is also possible that her salary (and/or her husband's salary) is also subject to NY state taxes due to his or her work site being located in NY state. If that is the case, the credit offered by NJ for taxes paid to another state may completely offset her NJ state tax liability. She (and her husband if they file jointly) would still have to file a NJ state tax return, but no taxes would be owed.