How to convert Timestamp to Date Data Type in Google Bigquery

If you use Standard SQL, you can do the following:

SELECT * REPLACE(EXTRACT(DATE FROM curr_dt)) AS curr_dt FROM test.date_table

If curr_dt is repeated field, then the solution will look the following:

SELECT * REPLACE(
  ARRAY(
    SELECT EXTRACT(DATE FROM curr_dt) FROM t.curr_dt
  ) AS curr_dt)
FROM test.date_table t

Consider below!
Works in both Legacy and Standard SQL

SELECT CAST(DATE(CURR_DT) AS DATE) AS CURR_DT FROM TEST.DATE_TABLE

Added to address comment

Try below - as I mentioned above - it works for both Legacy and Standard

SELECT CAST(DATE(CURR_DT) AS DATE) AS CURR_DT
FROM (SELECT CURRENT_TIMESTAMP() AS CURR_DT)  

if you are interested in making your case working with Legacy SQL - provide more details about CURR_DT field