Since you're using ADO.NET, you can use ADO.NET's inbuilt connection pooling capabilities. Actually, let me refine that: you must always use ADO.NET's inbuilt connection pooling capabilities. By doing so you will get the .NET runtime to transparently manage your connections for you in the background. It will keep the connections open for a while even if you closed them and reuse them if you open a new connection. This is really fast stuff.
Make sure to mention in your connection string that you want pooled connections as it might not be the default behaviour.
You only need to create connections locally when you need them, since they're pooled in the backrgound so there's no overhead in creating a new connection:
using (var connection = SomeMethodThatCreatesAConnectionObject())
{
// do your stuff here
connection.Close(); // this is not necessary as
// Dispose() closes it anyway
// but still nice to do.
}
That's how you're supposed to do it in .NET.