You should be able to get the data by querying (Tooling API):
SELECT Metadata FROM CustomField WHERE TableEnumOrId = '<Table Name>' AND DeveloperName = '<FieldName>'
The valueSet
attribute of the Metadata
field will contain the name of the global picklist used, if any.
Example (40.0):
{
"size" : 1,
"totalSize" : 1,
"done" : true,
"queryLocator" : null,
"entityTypeName" : "CustomField",
"records" : [ {
"attributes" : {
"type" : "CustomField",
"url" : "/services/data/v40.0/tooling/sobjects/CustomField/00N500000041HS5EAM"
},
"Metadata" : {
... // excluded for brevity
"valueSet" : {
"controllingField" : null,
"restricted" : true,
"valueSetDefinition" : null,
"valueSetName" : "A",
"valueSettings" : null
},
"visibleLines" : null,
"writeRequiresMasterRead" : null
}
} ]
}
Note that this will be the "developer" name of the valueSet. So, for example, above, my value set is called "A".