Connections are expensive, meaning in time and resources. Depending upon the system you are creating and the database you are using you may want to open the connection when the program starts and close the connection when the program ends, which is the easiest way in which to do things. Then when it comes to recordsets, you only keep them open for as long as you need them as they are expensive in their own right and can be even more expensive than a connection object...
Also, you use the pretty much the same syntax in closing a connection as you do with a recordset...
adoRs00.Close
Set adoRs00 = Nothing
adoCn00.Close
Set adoCn00 = Nothing
Good Luck