...
http://YOURDOMAIN/plugins/servlet/crm/api?command=searchEntities&crm_param_1=Company&crm_param_1_value=Teamlead&tableName=CONTACTS&userName=${userName}&apiKey=${apiKey}
Edit contact:
http://YOURDOMAIN/plugins/servlet/crm/api?command=editcontact&apiKey=${apiKey}&userName=${userName}&contactId=${contactId}&view-clients-contact_position=${position}&clients-contact_position=${position}&clients-contact_email=${email}&clients-contact_login=${userName}
Edit companyPass value parameters to the api methods by field codes or by field names:
http://YOURDOMAIN/plugins/servlet/crm/api?command=editcompany&apiKey=${apiKey}&userName=${userName}&companyId=${companyId}&view-clients-clients_field_d1facd51-01e0-4a68-a4f3-4aa3641a590e=Development,Training&clients-clients_field_d1facd51-01e0-4a68-a4f3-4aa3641a590e=Development,Training
http://YOURDOMAIN/plugins/servlet/crm/api?command=editcompany&apiKey=${apiKey}&userName=${userName}&companyId=${companyId}&clients-clients_field_d8927b73-09ba-4094-b281-af6738e4432d=testest
http://YOURDOMAIN/plugins/servlet/crm/api?command=editcompany&apiKey=${apiKey}&userName=${userName}&companyId=${companyId}&Сompany name=${companyName}
where:
${apiKey} - API Key (password) in the Administration/Plugins/CRM/Access${userName} - JIRA user's login