No, it isn't necessary unless your state requires it, most states say either lights or reflectors, not many say reflectors are required regardless if you have lights or not.
Reflectors are ok, problem is though they're too independent upon the angle of the cars headlights as to whether or not the reflectors will work, in most cases a motorist won't even see you till they're on top of you. I'm not saying not to use passive lighting, what I'm trying to say is not count on passive lighting, you need to be using active lighting and counting on that instead. So put your money first into active lighting, todays prices on LED lights are crazy low, you can get a 500 lumen light and a 300 lumen tail light for under $90, it's silly not to do that, and those lights are so bright a motorists can even readily see you in broad daylight from a distance.
Most cycling clothing, shoes, saddle bags etc., these come with passive lighting built into the stuff, do you need to add more? The only thing I would add at night is a pair of highly reflective ankle bands, and a neon colored (yellow or orange) mesh vest with the wide reflective bands in them that cost around $19 or so if you really want to make sure you got the best of both worlds. But that's all I would add in regards to reflectors.
Everyone will have their own opinion, that's fine, this subject is purely opinion, but you can read this for more info:
https://www.bicycling.com/bikes-gear...-safer-riding/
The other weird thing about lights is that a study done at night in Europe showed that a steady rear light is better because motorists could tell how far they were from a cyclist vs a flashing one, so in parts of Europe it's against the law to use a flashing light. HOWEVER, in Canada their study showed that a flashing light was better then a steady because it attracted the motorists attention faster. What to do you scream? simple! Just use two lights in the rear, one on flashing and the other on steady; you can do the same thing with two headlights.