Month-To-Month Rent Raise Question!

[Justin Gomberg]

Hello all! 

I just recently closed on my third property (first duplex...yay!) This was managed by a PM prior and one of the units is on a month-to-month lease. I was curious what the right way to increase the rent is? 

I intend on giving them a 60-day notice on 05/01/2021 informing them of the rent change. If the tenants are ok with the rent increase and choose not to move out, is it customary to just start collecting the higher rent or at the start of the rent increase have them sign a new lease associated with me the new owner? 

I would feel more comfortable requiring them to sign a new lease at the start of the rent increase. 

If I decide to have them sign a new lease am I allowed to request their w-2 information and run background on them? I take screening tenants very seriously and hate that I assumed full responsibility for tenants I was never able to screen initially.

Thank you for all of your awesome help in advance!