The authority for the Delaware Background Check Center can be found in Delaware Code:

For Nursing and Similar Facilities at 16 Del.C. §§1141 and 1142 and 29 Del.C. §7972.
Title 16 1141 1142

For Training Programs, Temporary Agencies and Home Health Agencies at 16 Del.C. §§1145 and 1146 and 29 Del.C. §7972.
Title 16 1145 1146 

Section 182.

Any non-state agency whose employees are required to receive criminal background checks pursuant to 16 Del. C. § 1141 and § 1145, shall provide to the Department of Health and Social Services quarterly reports including a list of all employees hired over the preceding quarter for the purposes of verification. The Department of Health and Social Services shall review those lists to ensure compliance with 16 Del. C. § 1141 and § 1145. 

The reports shall be submitted to the Division of Health Care Quality within 30 days of the end of the preceding quarter.  Please submit reports to the Background Check Center at DHSS_DLTCRP_BCC@delaware.gov