From the Guidelines

Calcium supplementation is not recommended for postmenopausal women.

The U.S. Preventive Services Task Force (USPSTF) concludes that the current evidence is insufficient to assess the balance of the benefits and harms of combined vitamin D and calcium supplementation for the primary prevention of fractures in noninstitutionalized postmenopausal women 1.
The USPSTF recommends against daily supplementation with 400 IU or less of vitamin D3 and 1000 mg or less of calcium for the primary prevention of fractures in noninstitutionalized postmenopausal women, citing a lack of net benefit and potential harms such as an increased incidence of renal stones 1.
Some studies suggest that high doses of vitamin D3 may have modest beneficial effects on calcium absorption, but the evidence is limited and the interaction between calcium and vitamin D intake is complex and not fully understood 1.

The USPSTF recommendations apply to noninstitutionalized or community-dwelling asymptomatic adults without a history of fractures, and do not apply to persons with osteoporosis or vitamin D deficiency 1.
The potential harms of calcium supplementation, including an increased incidence of renal stones, must be weighed against the potential benefits, which are currently unclear 1.
Clinicians should individualize decision making to the specific patient or situation, taking into account the evidence and other considerations such as patient preferences and medical history 1.

From the Research

The North American Menopause Society recommends adequate calcium intake (at least 1,200 mg/day) for postmenopausal women to prevent bone loss and reduce fracture risk 2, 3.
Calcium supplementation has been associated with beneficial effects in several nonskeletal disorders, including hypertension, colorectal cancer, obesity, and nephrolithiasis 2, 3.
Vitamin D status is also important, with a daily intake of 400-600 IU recommended to ensure adequate calcium absorption 2, 3.

The target calcium intake for most postmenopausal women is 1,200 mg/day 3.
Estimates of adequate intakes of calcium for peri- and postmenopausal women are based on evidence relating to osteoporosis prevention, with at least 1,200 mg/day required for most women 2.
Levels greater than 2,500 mg/day are not recommended 2.

Calcium supplementation may reduce bone loss and fracture risk in postmenopausal women, particularly those with low calcium intakes 4, 3.
However, some studies have found that calcium supplementation may not significantly reduce fracture risk in postmenopausal women, and may even increase the risk of renal stones and gastrointestinal problems 5, 6.
The US Preventive Services Task Force recommends against daily supplementation with 400 IU or less of vitamin D and 1000 mg or less of calcium for the primary prevention of fractures in community-dwelling, postmenopausal women 6.