Easiest way to check for the existence of a constraint (and then do something such as drop it if it exists) is to use the OBJECT_ID() function...
IF OBJECT_ID('CK_ConstraintName', 'C') IS NOT NULL
ALTER TABLE dbo.[tablename] DROP CONSTRAINT CK_ConstraintName
OBJECT_ID can be used without the second parameter ('C' for check constraints only) and that may also work, but if your constraint name matches the name of other objects in the database you may get unexpected results.
IF OBJECT_ID('CK_ConstraintName') IS NOT NULL
ALTER TABLE dbo.[tablename] DROP CONSTRAINT CK_ConstraintName
OBJECT_ID can also be used with other "constraints" such as Foreign Key constraints or Primary Key constraints, etc. For best results, always include the appropriate object type as the second parameter for the OBJECT_ID function:
Constraint Object Types:
C = CHECK constraint
D = DEFAULT (constraint or stand-alone)
F = FOREIGN KEY constraint
PK = PRIMARY KEY constraint
R = Rule (old-style, stand-alone)
UQ = UNIQUE constraint
