Let's assume that you have a simple userform with check boxes and a command button with default names, and in the document you have inserted check box content controls with tags of Check1 and Check2 etc. The userform code would be 
Option Explicit

Private Sub CommandButton1_Click()
    Me.Hide
    Me.Tag = 1
End Sub
In an ordinary module the following macro would call the form and process two check boxes - add as many other check boxes as required using similar syntax.

Option Explicit
Sub RunUserform()
Dim oFrm As New UserForm1
Dim oCTRL As ContentControl
    With oFrm
        .Show
        If .Tag = 1 Then
            For Each oCTRL In ActiveDocument.ContentControls
                If oCTRL.Type = wdContentControlCheckBox Then
                    oCTRL.Checked = False
                End If
            Next oCTRL
            If .CheckBox1.Value = True Then
                For Each oCTRL In ActiveDocument.ContentControls
                    If oCTRL.Tag = "Check1" Then
                        oCTRL.Checked = True
                        Exit For
                    End If
                Next oCTRL
            End If
            If .CheckBox2.Value = True Then
                For Each oCTRL In ActiveDocument.ContentControls
                    If oCTRL.Tag = "Check2" Then
                        oCTRL.Checked = True
                        Exit For
                    End If
                Next oCTRL
            End If
        End If
    End With
    Unload oFrm
    Set oFrm = Nothing
End Sub