Proximal Attachment
The second intercostal intimus muscle may be absent but when present lies deep to the second intercostal internus in the middle two-quarters of the intercostal space.  It is an insignificant muscle that arises from the internal aspect of the second rib.

Distal Attachment
Anteriorly the fibers pass infero-laterally, while posteriorly they pass infero-medially to insert onto the internal aspect of the third rib.  

Nerve Supply
The second intercostal intimus muscle is supplied by the second intercostal nerve.

Action
The second intercostal intimus is most active during expiration, but its primary role is with the second intercostal externus to stiffen the chest wall during respiration.