T-SQL Query - Find simple and complex record

do you mean this?

--drop table #temp
create table #temp(Key_Column VARCHAR(50),      Start_Date DATETIME,    End_Date DATETIME,      status VARCHAR(50))
insert into #temp (Key_Column,  Start_Date,     End_Date,       status) VALUES
('K1','2015-03-02 00:00:00.000','2016-03-02 00:00:00.000',NULL),
('K1','2016-03-15 00:00:00.000','2015-03-02 00:00:00.000',NULL),
('K2','2015-03-02 00:00:00.000','2016-03-02 00:00:00.000',NULL),
('K2','2016-03-15 00:00:00.000','2016-04-15 00:00:00.000',NULL),
('K2','2018-03-02 00:00:00.000','2018-04-02 00:00:00.000',NULL)
;With CTE
AS
(
SELECT *,ROW_NUMBER() OVER (PARTITION BY key_Column ORDER BY Start_date,End_Date) AS Rn
FROM #Temp),CTE1
AS
(
SELECT c1.Key_Column
FROM CTE c1
INNER JOIN CTE c2
ON c2.Key_Column = c1.Key_Column
AND c2.Rn = c1.Rn + 1
AND c2.Start_Date > DATEADD(dd,90,c1.End_Date)
)
UPDATE t
SET Status = CASE WHEN c.Key_Column IS NOT NULL THEN 'Complex' ELSE 'Simple' END
FROm #temp t
LEFT JOIN CTE1 c
ON c.Key_Column = t.Key_Column
SELECT * FROM #Temp

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