retirement/part time work

I'm 77 and have a qualified pension plan monthly pymnt of less than $100. I will receive this amt til I die.

This year I also earned about $3000 from taking care of another senior, for which I received a w-2, but no federal taxes were withheld.  When I go thru the turbo tax questions,  I actually end up not owing any federal taxes at all.  When I do the State return I get a $200 refund.  Am I required to file federal even though I owe nothing?  Can I just file the state?  Or is it a good idea to go ahead and file both of the returns?