Global Database Connection In .net?

I've inherited an application that uses a global database sqlconnection object in order to access the database from every form in the application. The connection is established when the application starts.I think to have the connection open all the time it's not good practice and I would prefer to change it so I would open the database connection and close it every time I need to access the database.

Public Sub UpdateDatabase(ByVal command As SqlCommand, ByRef NumError As Double, ByRef DescError As String)
Using connection As New SqlConnection(connectionString)
Try
command.ExecuteNonQuery()

[code].....

I send the SqlCommand object to the method instead of a query string because I can add parameters to an SqlCommand object.