Well....."No" would be the answer to your staright question. There is no direct link connection between LW(Gnutella) and any law enforcement agency.
However, any activity involving your computer(+internet connection) will be recorded and stored for a certain period of time with your Internet Service Provider (ISP). Those datas could be, theoretically, obtained by the police or by any other law enforcement agency.
To ease your concerns a little bit, I've been using some P2P clients for quite some time and yet no SWAT Team has arrived in front of my door.....
