Selecting Multiple Values from a Dropdown List in Google Spreadsheet

To Add to AlexG's answer, a better and enhanced version of multi-select is found in this following link (which I tried and worked as expected):

https://gist.github.com/coinsandsteeldev/4c67dfa5411e8add913273fc5a30f5e7

For general guidance on setting up a script in Google Sheets, see this quickstart guide.

To use this script:

1. In your Google Sheet, set up data validation for a cell (or cells), using data from a range. In cell validation, do not select 'Reject input'.
2. Go to Tools > Script editor...
3. In the script editor, go to File > New > Script file
4. Name the file multi-select.gs and paste in the contents of multi-select.gs. File > Save.
5. In the script editor, go to File > New > Html file Name the file dialog.html and paste in the contents of dialog.html. File > Save.
6. Back in your spreadsheet, you should now have a new menu called 'Scripts'. Refresh the page if necessary.
7. Select the cell you want to fill with multiple items from your validation range.
8. Go to Scripts > Multi-select for this cell... and the sidebar should open, showing a checklist of valid items.
9. Tick the items you want and click the 'Set' button to fill your cell with those selected items, comma separated.

You can leave the script sidebar open. When you select any cell that has validation, click 'Refresh validation' in the script sidebar to bring up that cell's checklist.

The above mentioned steps are taken from this link

I have found solution at https://www.youtube.com/watch?v=dm4z9l26O0I

You would need to use Tools > Script Editor. Create .gs and .html files there. See example at http://goo.gl/LxGXfU (link can be also found under Youtube video). Just copy

Once you have .gs and .html files in place save them and reload your spreadsheet. You will see "Custom menu" as the last item of your top menu. Select cell you would like to manage and click on this menu item.

During the first time it will ask you to authorize application - go ahead and do this.

Note (1): make sure that your cell has "Data validation" defined before you click on "Custom menu".

Note (2): it appeared that solution works with "List from a range" criteria for Data validation (it does not work with "List of items")

I have found a great work-around for this. It really only works practically if you want to be able to select up to 4 or so options from your drop down list but here it is:

For each "item" create as many rows as drop-down items you'd like to be able to select. So if you want to be able to select up to 3 characteristics from a given drop down list for each person on your list, create a total of 3 rows for each person. Then merge A:1-A:3, B:1-B:3, C:1-C:3 etc until you reach the column that you'd like your drop-down list to be. Don't merge those cells, instead place the your Data Validation drop-down in each of those cells.

Hope this is clear!!

I see that you've tagged this question with the google-spreadsheet-api tag. So by "drop-down" do you mean Google App Script's ListBox? If so, you may toggle a user's ability to select multiple items from the ListBox with a simple true/false value.
Here's an example:

var lb = app.createListBox(true).setId('myId').setName('myLbName');

Notice that multiselect is enabled because of the word true.