Below are few info, yes you do need to get employment offer letter from the company you want to do CPT in. For that, get a job in that company first( search company, send resume, appear for interview yadi yada yada...
). I got following info from my schools web page. You might want to contact your career services in ur school.
Co-op Specifics for International Students
Co-op is considered Curricular Practical Training (CPT) for international students and is available to those with the F-1 visa status. To participate, students with the F-1 visa status must first complete one academic year of consecutive fulltime enrollment in a U.S. school.
F-1 Co-op Regulations and Work Options
International students must take courses while working a Co-op position. The only exceptions are during the graduating and Summer semesters. The I-20 is endorsed before students start to work.
Part-time: 16 - 20 hours per week, requires that undergraduates have 12 hours and graduates have 9 hours.
Full-time: 21 - 40 hours/week, requires that undergraduates have 9 hours and graduates have 6 hours.
Only 3 hrs of coursework can be web-based or online.
Work Authorization
Students with the F-1 visa status can work without employer sponsorship. College sponsors the student and handles any paperwork with Curricular Practical Training and Optional Practical Training.
An F-1 student can work three semesters in Curricular Practical Training as long as the student’s Candidate Plan of Study permits.
International students who exceed 12 months aggregate fulltime CPT will lose Optional Practical Training (OPT). Contact International Student Advisors in Admissions for more information about OPT.
Taxation of F-1 Student Wages
International students in Co-op pay income tax that is withheld by the employer. However, because students do not owe Social Security or Medicare tax, these should not be withheld from a paycheck.
No University employee can give tax advice to students or employers. Tax questions and requests for forms and publications may be directed to a local IRS office, calling the IRS or visiting the IRS website
