<form method="POST" action="/zcrm_leads">
   <label for="name">Name:</label>
   <br>
   <input type="text" id="name" name="name" value="">
   <br>
   <label for="phone">Phone:</label><br>
   <input type="text" id="phone" name="phones[0][phone]" value="">
   <br>
   <label for="phone">Email:</label><br>
   <input type="text" id="email" name="contacts[0][value]" value="">
   <br>
   <br>
   <input type="submit" value="Submit">
</form>

<?php
$postData = $_POST;
if ($postData) {
   if (isset($postData['phones'], $postData['phones'][0], $postData['phones'][0]['phone'])) {
       $postData['phones'][0]['type'] = 'work';
   }
   if (isset($postData['contacts'], $postData['contacts'][0], $postData['contacts'][0]['value'])) {
       $postData['contacts'][0]['type'] = 'email_work';
   }
   $params = ['lead' => $postData];
   $params['lead']['lead_source'] = 'form';
   $leadData = makePostRequest('/v1/zcrm/leads', $params);
   var_dump($leadData);
}
exit();
function makePostRequest($method, $params)
{
   // замените userKey и secret на ваши из личного кабинета
   $userKey = '';
   $secret = '';
   $apiUrl = 'https://api.zadarma.com';
   ksort($params);
   $paramsStr = makeParamsStr($params);
   $sign = makeSign($paramsStr, $method, $secret);
   $curl = curl_init();
   curl_setopt($curl, CURLOPT_URL, $apiUrl . $method);
   curl_setopt($curl, CURLOPT_CUSTOMREQUEST, 'POST');
   curl_setopt($curl, CURLOPT_POST, true);
   curl_setopt($curl, CURLOPT_CONNECTTIMEOUT, 10);
   curl_setopt($curl, CURLOPT_RETURNTRANSFER, true);
   curl_setopt($curl, CURLOPT_SSL_VERIFYPEER, false);
   curl_setopt($curl, CURLOPT_SSL_VERIFYHOST, false);
   curl_setopt($curl, CURLOPT_POSTFIELDS, $paramsStr);
   curl_setopt($curl, CURLOPT_HTTPHEADER, [
       'Authorization: ' . $userKey . ':' . $sign
   ]);
   $response = curl_exec($curl);
   $error = curl_error($curl);
   curl_close($curl);
   if ($error) {
       return null;
   } else {
       return json_decode($response, true);
   }
}
/**
* @param array $params
* @return string
*/
function makeParamsStr($params)
{
   return http_build_query($params, null, '&', PHP_QUERY_RFC1738);
}
/**
* @param string $paramsStr
* @param string $method
* @param string $secret
*
* @return string
*/
function makeSign($paramsStr, $method, $secret)
{
   return base64_encode(
       hash_hmac(
           'sha1',
           $method . $paramsStr . md5($paramsStr),
           $secret
       )
   );
}