Do a google and see if it's a Arizona cypress.

"Cedar" is a very confusing term when used in relation to junipers and I'd try to avoid it. But if it has cones, then it is a female juniper :-) No pollen! However, depending on species (could it be the more common in your area southwest native Juniperus ashei?), the male pollen can travel great distances with the wind, as much as 300 miles. Any male juniper in the vicinity can cause an allergy problem in those sensitive to it as well as fertilize your female to produce cones. Your neighbor shouldn't blame you for what occurs outside your property.

The attached link is a bit alarmist and one-sided in its approach and recommendations but it does explain the pollen issue and associated problems rather well.

Here is a link that might be useful: Juniper/'cedar' pollen allergies

dricha: no, it for sure is not an Arizona cypress ... we had those a few years ago & we sure got rid of them... tons of pollen!
Gardendgal: good to know now that the cones mean my tree is a female & NO pollen! The neighbor chose my tree because it was closest to condemn though down the street are many evergreens of ? sex. The City has outlawed the sale of Italian cypress (& I love those stately tall columnar trees!),mulberry, 'Chinese' elm (really 'Siberian' elm I believe here),Arizona cypress & Russian olive but of course the ones already here are OK ... just no new ones can be planted. The darn elm produce those tons of papery seeds that blow all over for miles & grow everywhere wild in the arroyos,etc. so that tree never will be eradicated. They were introduced years ago when the City needed some kind of tree that would survive our hot, dry climate & it was the only one available back then that fit the bill unfortunately. If it were not for the tons of seeds (& must be nearly 90% germination of those seeds too!) the tree is not bad looking & is hardy & surprizingly long-lived here.
Yes, the common 'cedars' as well as the Russian olive use so much of our precious water so ranchers are yanking them all down & the range grass then begins to spread again without the competition for water. The olive along the streams & rivers are being removed also for the same reason & let the native trees (cottonwood esp.)grow back.

My cedar is over 40 yrs. old & quite a haven for all kinds of birds... now I know it is a female & no pollen it will be a 'keeper' for sure!

Thanks everyone!