Man pages matching name curlopt_connecttimeout_ms in section 3:

CURLOPT_CONNECTTIMEOUT_MS.3.en	debian 10 / libcurl4-doc
CURLOPT_CONNECTTIMEOUT_MS.3.en	debian 11 / libcurl4-doc
CURLOPT_CONNECTTIMEOUT_MS.3.en	debian 12 / libcurl4-doc