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This is possible but undocumented I'm afraid.
Example configuration is following:
[BlockTypeName]
CustomAttributes[]=my_checkbox
CustomAttributeTypes[my_checkbox]=checkbox
Supported values for CustomAttributeTypes are following: text, checkbox, string. If not defined then string is default value.
For checkbox type GUI will render regular checkbox button with values 0 or 1.
Then in templates you can use it like
{if $block.custom_attributes.my_checkbox|eq('1')}
checked!
{else}
unchecked!
{/if}
Hope this helps!
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