Based on what described in the original post, assuming dummyDate is the value from the database table column. You can modify the code to check if the column is null, if yes, use the emptyDate else keep the selected date from the DateTimePicker control.
var dummyDate = DBNull.Value;
vrijemeodjaveDateTimePicker.Value =
DBNull.Value.Equals(dummyDate) ? emptydate : vrijemeodjaveDateTimePicker.Value;
Or maybe you meant to ask, how to set the DateTimePicker to a default value if the column value is NULL , else use the value from the database column.
vrijemeodjaveDateTimePicker.Value =
DBNull.Value.Equals(SomeValueFromDatabaseColumn) ? emptydate : SomeValueFromDatabaseColumn;