You should call curl_global_cleanup(3) once for each call you make to curl_global_init(3), after you are done using libcurl.
This function is not thread safe. You must not call it when any other thread in the program (i.e. a thread sharing the same memory) is running. This doesn't just mean no other thread that is using libcurl. Because curl_global_cleanup(3) calls functions of other libraries that are similarly thread unsafe, it could conflict with any other thread that uses these other libraries.
See the description in libcurl(3) of global environment requirements for details of how to use this function.