WPF MVVM TreeView SelectedItem

You should not really need to deal with the SelectedItem property directly, bind IsSelected to a property on your viewmodel and keep track of the selected item there.

A sketch:

<TreeView ItemsSource="{Binding TreeData}">
    <TreeView.ItemContainerStyle>
        <Style TargetType="{x:Type TreeViewItem}">
            <Setter Property="IsSelected" Value="{Binding IsSelected}" />
        </Style>
    </TreeView.ItemContainerStyle>
</TreeView>

public class TViewModel : INotifyPropertyChanged
{
    private static object _selectedItem = null;
    // This is public get-only here but you could implement a public setter which
    // also selects the item.
    // Also this should be moved to an instance property on a VM for the whole tree, 
    // otherwise there will be conflicts for more than one tree.
    public static object SelectedItem
    {
        get { return _selectedItem; }
        private set
        {
            if (_selectedItem != value)
            {
                _selectedItem = value;
                OnSelectedItemChanged();
            }
        }
    }

    static virtual void OnSelectedItemChanged()
    {
        // Raise event / do other things
    }

    private bool _isSelected;
    public bool IsSelected
    {
        get { return _isSelected; }
        set
        {
            if (_isSelected != value)
            {
                _isSelected = value;
                OnPropertyChanged("IsSelected");
                if (_isSelected)
                {
                    SelectedItem = this;
                }
            }
        }
    }

    public event PropertyChangedEventHandler PropertyChanged;
    protected virtual void OnPropertyChanged(string propertyName)
    {
        var handler = this.PropertyChanged;
        if (handler != null)
            handler(this, new PropertyChangedEventArgs(propertyName));
    }
}