Public Class TuaClasse
  'Dichiarando qui puoi vederla in tutti i metodi della classe
  Private objconnection As New SqlConnection
  
  Public Sub apriConnessione()
    objconnection = New SqlConnection()
    objconnection.ConnectionString = "Data Source=.\SQLEXPRESS;AttachDbFilename=C:\Documenti\CCRM.mdf;Integrated Security=True;Connect Timeout=30;User Instance=True"
    objconnection.Open()
  End Sub
  ...
End Class