Incearcă ceva de genul:

DECLARE @pData DATETIME = GETDATE()

DECLARE @primaZi DATETIME = DATEADD(MONTH,DATEDIFF(MONTH,0,@pData),0)
DECLARE @ultimaZi DATETIME = DATEADD(MONTH,DATEDIFF(MONTH,-1,@pData),-1)

SELECT * FROM persoane WHERE data_incep <= @ultimaZi AND data_sfarsit >= @primaZi

Razvan