From what I understand, the test results aren't published anywhere online - instead Suffolk County ensure that the scores are sent out to each individual candidate once they have been graded.
There's no fixed amount of time that this should happen in, but I wouldn't anticipate waiting more than a couple of weeks.
If you're anxious to get more info, or have been waiting for an unordinary amount of time without having heard anything, then I'd suggest first checking out their sites FAQ section here: http://www.suffolkcountyny.gov/departments/civilservice.aspx
Otherwise, these are the contact details you'll need for further enquiries:
Alan Schneider
Personnel Director
Address:Bldg. 158, North County Complex
PO Box 6100
Hauppauge, NY 11788-0099
Phone: (631) 853-5500
Fax: (631) 853-4796
Email: Civil Service