From NRA-ILA:

SB 53 would require the purchasers of ammunition to register with the state Department of Justice (DOJ) prior to purchasing any ammunition.  This registration would require the submission of fingerprints, a background check and fees to the DOJ.  If passed and enacted into law, SB 53 would require the collection and reporting of personal consumer information and thumbprinting for all ammunition purchases throughout the state.  It would also ban online and mail-order sales of all ammunition, including hunting and collectible ammunition.  In addition, SB 53 would require anyone wishing to exercise their fundamental right to keep and bear arms to obtain a costly ammunition purchaser permit that must be renewed every two years.

Read the bill here

From smartgunlaws.org:

Status: This bill passed the Assembly Public Safety Committee on June 10, and is currently on the Assembly floor.