Children born on the Island to expats are not automatically entitled to citizenship, unless one or both of their parents are either Caymanian or have been granted status or Permanent Residency.
For more information see Cayman Parent's articles on Registering the Birth of Your Child Born in Cayman and Immigration Rules for Kids.
If you are on a work permit, your baby must be added as a dependant on your work permit.
You can find the AMD2 ‘Dependant Information Form Checklist’ (aka the RV37a) on www.worc.gov.ky which outlines the things you need to gather and submit. These include the application filing fee of CI$100 and a separate grant fee of CI$500, which is payable on approval. The required supporting documents include employment letters in relation to each parent and a ‘Monthly Income and Expense Report’ with which the Dept. of WORC will decide whether you can afford to have a dependant stay in Cayman with you.
It is generally accepted that your minimum monthly base salary for a family of three must be in the region of CI$3,500. You will generally be expected to earn an extra CI$500 to CI$1,000 per month for each additional dependant.
When all the requirements are met, your child’s passport (once issued) will get a stamp with a date on it.
Remember to get each new passport re-stamped as airlines need to see an up-to-date dependant stamp in the passport when you travel.
If you have any questions, call WORC on (345) 949 8344 or visit their website.