In both constructors you're using local variable
SQLiteConnection SQLconnect = new SQLiteConnection();
which goes out of scope after the constructor finishes. You have to create class member variable:
public partial class Form1 : Form
{
SQLiteConnection _SQLconnect;
public Form1()
{
Data_connection dbobject = new Data_connection();
_SQLconnect = new SQLiteConnection();
InitializeComponent();
}
}