There are two ways to create a constraint,
Method A:
ALTER TABLE dbo.<tablename> ADD CONSTRAINT
<namingconventionconstraint> UNIQUE NONCLUSTERED
(
<columnname>
Method B:
CREATE UNIQUE NONCLUSTERED INDEX
<namingconventionconstraint> ON dbo.<tablename>
(
<columnname>
) ON [PRIMARY]
However, it appears that these constraints need to be dropped using a method that is dependent on how they were created (Drop constraint vs drop index). Is there a way to determine what method the constraint was created other than trying a method and seeing if it fails? I know you can have SQL Server create a drop script for you but I'm looking for a query of some sort.